Personal Model of Conflict Resolution

For this assignment, you will research what is meant by a conflict resolution model. Your final product will be a 3- to 4-page Microsoft Word document with a relevant and usable model illustrating the dynamic process of conflict resolution specific to interpersonal conflict scenarios that provides detailed support for your model.

Personal Model of Conflict Resolution

For this assignment, you will research what is meant by a conflict resolution model. Research at least four scholarly sources to examine at least two such models. Then, create your own version of a conflict resolution model, incorporating information from the two models you researched. You should include a description of your model’s components and provide an explanation as to how someone would utilize this model. Be sure to also include a visual illustration (a concept map, a chart, a diagram, a figure, etc.) of what the model would look like.

Your final product will be a 3- to 4-page Microsoft Word document with a relevant and usable model illustrating the dynamic process of conflict resolution specific to interpersonal conflict scenarios that provides detailed support for your model. Make sure you write in a clear, concise, and organized manner; demonstrate ethical scholarship in accurate representation and attribution of sources; and display accurate spelling, grammar, and punctuation.

Discussion Grading Table

Maximum Points

Researched and briefly described two existing conflict resolution models.

Created your own version of a conflict resolution model.

Included a description of your model’s components.

Provided an explanation as to how someone would utilize your model.

Included a visual illustration of what the model would look like.

Wrote in a clear, concise, and organized manner; demonstrated ethical scholarship in accurate representation and attribution of sources; and displayed accurate spelling, grammar, and punctuation.

International Journal of

Environmental Research

and Public Health

Article

An Improved Graph Model for Conflict Resolution
Based on Option Prioritization and Its Application

Kedong Yin 1,2, Li Yu 1 ID and Xuemei Li 1,2,*
1 School of Economics, Ocean University of China, Qingdao 266100, China; yinkedong@ouc.edu.cn (K.Y.);

yuli920718@163.com (L.Y.)
2 Ocean Development Research Institute, Major Research Base of Humanities and Social Sciences of Ministry

of Education, Ocean University of China, Qingdao 266100, China
* Correspondence: lixuemei@ouc.edu.cn, Tel.: +86-185-6135-4087

Received: 7 September 2017; Accepted: 18 October 2017; Published: 27 October 2017

Abstract: In order to quantitatively depict differences regarding the preferences of decision makers for
different states, a score function is proposed. As a foundation, coalition motivation and real-coalition
analysis are discussed when external circumstance or opportunity costs are considering. On the basis
of a confidence-level function, we establish the score function using a “preference tree”. We not only
measure the preference for each state, but we also build a collation improvement function to measure
coalition motivation and to construct a coordinate system in which to analyze real-coalition stability.
All of these developments enhance the applicability of the graph model for conflict resolution (GMCR).
Finally, an improved GMCR is applied in the “Changzhou Conflict” to demonstrate how it can be
conveniently utilized in practice.

Keywords: graph model for conflict resolution; sustainable development on conflict analysis;
option prioritization; real-coalition stability analysis

1. Introduction and Motivation

Conflict analysis is a branch of game theory, and the graph model is an important method for
solving conflict. The basic idea is to use related knowledge of subsets and graph theory to obtain an
equilibrium state. Fraser and Hipel simplified metagame analysis and developed it into published
work on F-H conflict analysis [1,2]. Later, Kilgour et al. continued this work and evolved it into the
graph model for conflict resolution (GMCR) [3], which they described comprehensively and minutely.

Since it was first proposed, scholars have studied GMCR from multiple perspectives: decision
makers (DMs) who hold different attitudes and emotions would have different effects on the results of
conflict. Walker et al. used the attitude of DMs as a foundation on which to construct four preferences
and four stabilities [4]. Obeidi et al. considered emotion as an essential modifier in conflict analysis, and
used the example of U.S.–North Korea conflict to demonstrate that the graph model could be simplified
after taking emotion into account [5]. Research on the preferences of DMs generally considers four
aspects: fuzzy preferences, gray preferences, strength of preferences, and unknown preferences.
Mubarak et al. proposed an improved method for fuzzy preference that was based on DMs holding
five different preference degrees on feasible states. Furthermore, they quantified the preference degree
for each DM through piecewise functions and redefined the four stabilities. They then resolved the
conflict and achieved an equilibrium state [6]. Option prioritization was first proposed by Wang
and Hipel [7]. Thereafter, Bashar put forward the definition of fuzzy truth value and improved
option prioritization [8]. Yu and Yu researched fuzzy preference further, constructing a framework
for calculating fuzzy preferences of DMs and applying it to practical conflict [9]. Kuang et al. [10]
determined the preference sequence by using a gray-based preference structure and redefined gray

Int. J. Environ. Res. Public Health 2017, 14, 1311; doi:10.3390/ijerph14111311 www.mdpi.com/journal/ijerph

http://www.mdpi.com/journal/ijerph

http://www.mdpi.com

https://orcid.org/0000-0003-1500-9924

http://dx.doi.org/10.3390/ijerph1411131

http://www.mdpi.com/journal/ijerph

Int. J. Environ. Res. Public Health 2017, 14, 1311 2 of 15

stabilities. They then applied the improved model to a brownfield conflict in Ontario, Canada. The
interval gray number was used by Yang and Guan to determine preference ranking and was applied to
industry–university cooperation conflict [11]. Liu continued an intensive study into the combination
of gray number and GMCR to solve equilibrium states and decision paths [12]. Hamouda et al. [13]
extended DM preference to a triplet preference structure. They generalized the basic concept on a
subset and then refined strong and weak stability. Finally, the strength of preference was applied to a
water conflict.

Kevin and Hipel considered uncertain preference as a potential improvement. They redefined the
formal definition and enhanced the applicability of the graph model by proposing an algorithm to
generate a status quo diagram and table. They then analyzed an environmental conflict to demonstrate
how the new algorithm could be applied [14]. Yu and Hipel redefined two logical connectives to
determine an unknown preference, and applied it to a water dispute [15]. With respect to coalition
analysis, Kilgour et al. depicted the fundamental definitions of coalition analysis in detail, and
illustrated the procedure in GMCR II with a simple model [16]. Kinsara and Kilgour introduced
third-party intervention to GMCR and constructed inverse GMCR to measure how third parties
influence the process of conflict [17]. Kinsara and Hipel preferred three approaches to improve and
simplify the understanding of conflict results [18].

The process of solving GMCR is concise, and the procedure is clear, so it is widely used
in negotiation support, water resource protection, brownfields, complex products, sustainable
development, energy, and other fields. Hipel and Kilgour used a Canadian groundwater storage
conflict as an example, elaborating the application of GMCR in solving environmental conflict in
detail [19]. Karnis et al. used GMCR to analyze the conflict in relation to the international upper great
lakes [20]. Huang and Liu expounded the definition of seven types of stability and expanded the
application of GMCR to business negotiations [21]. Wang and Kilgour put forward a risky project
negotiation framework to measure market risk and provide a resolution of conflict [22]. Kuang
and Bashar constructed a gray preference to express DM preference and used it to resolve conflict
over brownfield redevelopment [23]. Han and Xu extended the application of the graph model to
the complex process of aerospace products. In addition, they reconsidered the equilibrium state of
simple preferences based on the economic and corporation-reputation orientation of DMs [24]. Chu
and Hipel provided a win-win resolution for the Zhanghe River water-allocation dispute in China
through GMCR [25]. Li and Han made use of Matrix Representation of the Solution Concept (MRSC),
a decision-making system, to analyze credit expansion and concentration based on GMCR [26].

Currently, in the decision-support system GMCR II, there are three simple preference-ordering
methods for feasible states: direct rank, option weight, and option prioritization. For option
prioritization, each DM’s preference statements are listed in order of priority, often represented
vertically from the most important to least [27]. Option prioritization is a very useful preference
modeling technique and overcomes the limitations of other methods [26]; however, option
prioritization also has its shortcomings. In the vast majority of real-life situations, DMs cannot grasp
all the information, or also cannot hold a clear attitude on the issue of conflict, so when DMs express
their preference information, they usually do not have full confidence in every preference statement.
For instance, DMs definitely ensure the preference statements that are considered initially. As the
preference statements are represented one by one from the most important to the least important,
the DMs start to doubt the order and validity of preference statements, and this uncertainty will
gradually increase in the process of establishing preference statements. A higher confidence degree
of a preference statement means higher suitability, while a lower confidence degree of a preference
statement indicates a lower suitability. While this uncertainty in preference statements will affect
preference difference between different states. For two different states, the preference difference may
be either extremely small or severely large. Moreover, the uncertainty will affect coalition motivation
and will also affect the stability of the coalition.

Int. J. Environ. Res. Public Health 2017, 14, 1311 3 of 15

At present, the study on the fuzzy preference of decision makers has achieved fruitful
results [28–31]. However, there is little research on the uncertainty of preference statements. So,
this paper takes into account the DMs’ uncertainty in preference statements based on option
prioritization, and further measures the willingness and coalition stability. And the extended approach
is applied to “the conflict of Changzhou Foreign Language School”.

The remainder of the paper is structured as follows: the next section introduces the framework
of GMCR. An extended approach to design score function and real-coalition analysis is developed
in Section 3. A case study is provided in Section 4.

Conclusions

are presented in the final section of
the paper.

2. Framework of Graph Model for Conflict Resolution

The GMCR process includes modeling, stability analysis, and coalition analysis. The GMCR
itself consists of four basic components: DMs (N), feasible states (S), preference (P), and possible state
transitions (G). Each DM has its own options to choose or decide; Y indicates that the DM chooses
the option, whereas N means that it does not. Assemble all options that have been selected by an
individual DM as state s. Because not every state is achievable in the real world, the impossible
condition is appointed as an infeasible state. The subset excluding unfeasible states is the feasible states
subset S. Based on the GMCR framework, the concepts relating to subsets of states are summarized in
Table 1. Term P represents a feasible preference state sequence; feasible states are ordered by user or
a DM according the goal that the focal DM wants to achieve. Each DM has its own preference state
sequence. Since it is difficult for a user to obtain complete DM preference information about an actual
conflict event, preference is divided into four types: uncertainty preference, general preference, strong
preference, and multiple preferences. Term G exhibits state transition graph, where a state transition
means a DM unilaterally changes the option and shifts to another state.

Table 1. Concepts of subsets of states.

Subset of States Implication

Ri(s) The subset of states that DMi can unilaterally reach from state s.
R+i(s) The subset of states that DMi preferred to state s and can unilaterally reach from state s.
R=i(s) The subset of states that is equivalent to state s and can unilaterally reach from state s.
RH(s) The subset of states that coalition decision maker H can unilaterally reach from state s.

R+H(s) The subset of states that all coalition decision maker H preferred to state s and can unilaterally reach from state s.

DM: decision maker.

Each DM is rational and wants to achieve the most preferred state for itself. Decision makers only
make decisions about their own options, and are unable to intervene in those of others. The GMCR
predicts the state that is most likely to be accepted by all DMs; this state is known as the equilibrium
state. The course of solving for the equilibrium state is specified as stability analysis. There are four
basic stability formations in GMCR: Nash stability (R), general meta-rationality (GMR), symmetric
meta-rationality (SMR), and sequential stability (SEQ). If a stable state is reached by all DMs under
a certain stability, then it is an equilibrium state for conflict analysis. However, not all equilibrium
states can successfully solve conflict in the real world; we also need the user or DMs to judge and
analyze realities.

Path analysis can be used to find all states that DMs need to transit from the status quo to the
equilibrium state. There is often more than one path from the status quo to the equilibrium state;
the transition state and the number of steps are frequently diverse. Hence, the meaning of path analysis
is to find the shortest path, provide information for DMs to control the evolution of the conflict, improve
the efficiency and quality of decision-making, and solve the conflict effectively. In the transition route
to the equilibrium state, each DM can only transfer to the state that is preferred to its present state.
In other words, transition states belong to the subset of states that DMi can reach unilaterally from
state s. After achieving the equilibrium state, coalition analysis makes it necessary to identify whether

Int. J. Environ. Res. Public Health 2017, 14, 1311 4 of 15

the equilibrium state is still an equilibrium after considering cooperation. The purpose of coalition
analysis is to identify the equilibriums that are vulnerable to the action of a coalition that could achieve
another equilibrium preferred by all its members [16]. If the equilibrium state is not robust to the
consideration of a coalition, then equilibrium jumps will happen. This means the equilibrium state is
just temporary, and not a long-term equilibrium.

3. Score Function and Real-Coalition Analysis

The discussion outlined in the next subsection concerns the specified score function and
real-coalition analysis. The score function is used for quantify a DM’s state preference within the
GMCR. Subsequently, real-coalition analysis is defined to enhance the applicability of the graph model.

3.1. Score Function

Denote C as a DM’s level of confidence in its judgment of a preference statement. A higher value
of C implies that the preference statement is more suitable for all states, while a lower value of C
indicates that it is less appropriate:

Ct =

{
1, t ≤ p(

q+1−t
q+1−p

)g
, p + 1 ≤ t ≤ q

, g ∈{1, 2, · · · , n}, (1)

There are q preference statements in total; p is the critical point in judging preference statements,
and g is weight that decision maker consider the importance of the level of confidence. Form the
first to p-th preference statements, the DMs are fully confident in their judgments on preference
statements. Starting from the (p + 1)-th preference statement, the certainty of the DMs’ judgment
begins to weaken gradually.

Definition 1. Function (1) expresses DM confidence in the t-th preference statement and is the appointed
confidence level function.

To further highlight the priority weights of preference statements, one important task is to value
the preference statements. The priority of preference statements is defined as follow, according to the
“preference tree” idea put forward by Hipel.

Definition 2. αt is defined to express the priority of preference statements.
(
α > 0, α + α2 + α3 + . . . + αq < 1

)
and α ∈ [0, 1].

Apparently, higher-priority preference statements are given greater weight, and lower-priority
preference statements are given less weight.

In order to describe whether the state k of DMi complies with individual preference statements.

Definition 3. For all k ∈{1, 2, 3, · · · , n}, if sk conforms with preference statement Ωt, then σt = 1; if sk does
not meet the preference statement Ωt, then σt = 0, which can be represented in Equation (2).

σt(Ωt, Sk) =

{
1, True;
0, False;

(2)

Definition 4. For all preference statements, score function SC(sk) is defined to characterize the DM’s score at a
particular state sk, as shown in Equation (3)

SC(sk) = ∑
q
t=1

[
Ct

(
1
2

)t
σt(Ωt, Sk)

]
, for all k = 1, 2 . . . n (3)

Int. J. Environ. Res. Public Health 2017, 14, 1311 5 of 15

Score SC(sk) can be calculated for each feasible state for a particular DMi. The states can be
ranked according to their scores; a state with a higher score is preferred to a state with a lower score,
more specifically for s1, s2 ∈ S, s1 > s2 if and only if SC(s1) > SC(s2).

3.2. Real-Coalition Analysis with Two DMs

On the basis of calculating the score SC for each feasible state for a particular DMi, the differences
in coalition improvement can be captured. We can then compare the coalition motivation of each
DM and judge the strength of coalition stability. In this research, we consider a coalition with
two DMs temporarily.

In order to measure coalition motivation, a two-dimensional coordinate system needs to be
established to describe the reforming. We represent the equilibrium state, the coalition equilibrium
state, and the most preferred state in the coordinate system, as well as the corresponding score SC of
the three states. It is noticeable that the mapping relationship between states and scores is f: x→y = x.
As illustrated in Figure 1, the horizontal axis means the score of DMs in different states, and the vertical
axis represents states.

Int. J. Environ. Res. Public Health 2017, 14, 1311 5 of 14

In order to measure coalition motivation, a two‐dimensional coordinate system needs to be

established to describe the reforming. We represent the equilibrium state, the coalition equilibrium

state, and the most preferred state in the coordinate system, as well as the corresponding score of

the three states. It is noticeable that the mapping relationship between states and scores is f: x→y = x. As

illustrated in Figure 1, the horizontal axis means the score of DMs in different states, and the vertical

axis represents states.

Figure 1. Decision Makers’ (DMs’) Score Coordinate System.

Definition 5. The degree of Collation Improvement, denoted by is given by Equation (4).

,SC SC

∞, SC SC
SC SC , 0 (4)

From the geometric meaning, the value of corresponds to the ratio of segment SC SC and
segment SC SC . For DMi, when 1, the coalition equilibrium state’s score SC is located in
middle between SC and SC . At this point, the improved degree is moderate. When 1, SC is
closer to SC on the X axis, meaning that the coalition equilibrium state is closer to equilibrium state.
In other words, the improved degree is not as good as expected. When 1, SC is closer to SC

on the X axis, meaning that the coalition equilibrium state is closer to the most preferred state, i.e.,

the improved degree is more ideal. When ∞, the coalition equilibrium state is equal to the most
preferred state. This situation is the best result for coalition. In short, the degree of coalition

improvement is positively correlated with the value of .

Definition 6. For any subset ⊆ ,and | | 2, if state s in are those that can be attained from s by
a move by a member of H, or by a sequence of moves by members of H, then members of H are defined as a

coalition.

Definition 7. A state s∈ is coalition stable if and only if it is stable for all coalitions ⊆ .

For DMs, the motivated coalition identifies that all members of coalition prefer the target

state to the status quo [29]. So we have sufficient reason to weight the coalition motivation by a

coalition member’s that has been discussed above. Therefore, we can judge each DM’s willingness

and accurately describe the tendency of coalition formation, namely which DM will be more active.

For| | 2, a DM with a higher corresponds to a stronger coalition motivation, that is, a
greater willingness to form a coalition. In the process of forming a coalition, that DM will take the

initiative to communicate and convey the desire of coalition formation or take corresponding

strategies to facilitate coalition.

Figure 1. Decision Makers’ (DMs’) Score Coordinate System.

Definition 5. The degree of Collation Improvement, denoted by C I is given by Equation (4).

C I =

{
SC2−SC1
SC3−SC2

, SC2 6= SC3
+∞, SC2 = SC3

(SC1 6= SC2, and) C I ≥ 0 (4)

From the geometric meaning, the value of C I corresponds to the ratio of segment SC2SC3 and
segment SC1SC2. For DMi, when C I = 1, the coalition equilibrium state’s score SC2 is located in
middle between SC1 and SC3. At this point, the improved degree is moderate. When C I < 1, SC2 is closer to SC1 on the X axis, meaning that the coalition equilibrium state is closer to equilibrium state. In other words, the improved degree is not as good as expected. When C I > 1, SC2 is closer to SC3
on the X axis, meaning that the coalition equilibrium state is closer to the most preferred state, i.e.,
the improved degree is more ideal. When C I = +∞, the coalition equilibrium state is equal to the
most preferred state. This situation is the best result for coalition. In short, the degree of coalition
improvement is positively correlated with the value of C I.

Definition 6. For any subset H ⊆ N, and |H| = 2, if state s in SH(s) are those that can be attained from s by a
move by a member of H, or by a sequence of moves by members of H, then members of H are defined as a coalition.

Int. J. Environ. Res. Public Health 2017, 14, 1311 6 of 15

Definition 7. A state s ∈ S is coalition stable if and only if it is stable for all coalitions H ⊆ N.

For DMs, the motivated coalition identifies that all members of coalition H prefer the target state
to the status quo [29]. So we have sufficient reason to weight the coalition motivation by a coalition
member’s C I that has been discussed above. Therefore, we can judge each DM’s willingness and
accurately describe the tendency of coalition formation, namely which DM will be more active.

For |H| = 2, a DM with a higher C I corresponds to a stronger coalition motivation, that is,
a greater willingness to form a coalition. In the process of forming a coalition, that DM will take the
initiative to communicate and convey the desire of coalition formation or take corresponding strategies
to facilitate coalition.

Next, we will discuss real-coalition stability. If equilibrium jumps exist, then the decision support
system GMCR II will disseminate the outcome of coalition. However, in the real world, because of
external circumstances as well as the opportunity cost in the practice of coalition, DMs may not be
successful in forming a coalition. Even if the DMs can form a coalition, the interference of external
circumstances and non-coalition DMs or outsiders will possibly lead to the breakup of the coalition
relationship. In this section, we attempt to construct a paradigm based on the value of C I to measure
the possibility of coalition and the coalition relationship stability, and to make GMCR more in line
with the real world and have practical significance. The possibility and coalition relationship stability
that consider the external environment and the opportunity cost are defined as real-coalition stability.

If the values of C I for both coalition decisions are less than 1, i.e., C I(H1) < 1 and C I(H2) < 1, then the improvement degree is not good. Hence, in the process of coalescing, the two sides will conduct consultations and negotiations many times with high opportunity costs, thus sharply reducing the possibility of forming a coalition. Moreover, this situation can easily lead to coalition relations rupturing or a coalition being unable to evolve because of the obstruction of external circumstances and the temptation of interests by non-coalition DMs or other outsiders. Thus, the coalition relationship will break up effortlessly; hence, the real-coalition stability is poor.

Now suppose that the values of C I for both coalition decisions are greater than 1, i.e., C I(H1) > 1
and C I(H2) > 1 In that case, the real-coalition stability is steady and the degree of improvement is
very significant. Hence, both sides have a strong will to coalesce, and the coalition status will not be
interrupted by external conditions or other outsiders. In other words, the coalition relationship is tight.
If the C I value of one of two co-DMs is less than 1 or both are equal to 1, the real-coalition stability
is moderate.

4. Application of Improved GMCR

4.1. Background of Conflict and Modeling

With the purpose of improving its air quality, Changzhou New District launched the “Chang Long
Chemical” block chemical-industry seat relocation in May 2009, and formally implemented land
restoration in March 2014. The Changzhou Foreign Language School moved to a new campus adjacent
to the repaired block in September 2015; by the end of 2015, many of its students were in physical
discomfort. On 17 April 2016, the CCTV news channel reported the event headlined “Shouldn’t
Build School”, in which nearly 500 Changzhou Foreign Language School students showed signs of
physical discomfort. The suspected reason was that the school had been relocated close to the original
“Chang Long Chemical” industrial land. Individual students were even suffering from leukemia,
lymphoma, and other malignant diseases.

Experts said that the reason for the symptoms of discomfort was that the restoration operation
had not met specifications. The Black Peony Company was responsible for the land reparation project.
Its actual restoration method of “cover on spot” was not in accordance with the specified method
of “completely closed”, which resulted in the spread of pollution of volatile organic pollutants in
the soil. After the accident had been reported, the Government of Changzhou organized experts

Int. J. Environ. Res. Public Health 2017, 14, 1311 7 of 15

to design and carry out an emergency plan and an adjustment scheme. The event incited multiple
conflicts. In this study, we pay particular attention to the conflict that arose in relation to the health
problems of teachers and students at the Changzhou Foreign Language School (hereinafter called the
“Changzhou Conflict”).

The Environmental Protection Agency hoped to solve the environmental pollution problem
fundamentally. The Black Peony Company pursued revenue maximization of its enterprises.
The Government of Changzhou wanted to maximize the social and economic benefits under the
premise of ensuring the physical health of its teachers and students. The date selected for the GMCR II
analysis was 27 April 2016.

DMs and Options the—above-mentioned Changzhou Conflict was mainly related to three DMs:
the Environmental Protection Agency (EPA), the Black Peony Company (BPC), and the Government of
Changzhou (GC). The options of each DM are listed in Table 2.

Table 2. DMs and options in the Changzhou conflict.

Decision Makers (DMs) Options

EPA (DM1) 1. Supervise the process of field repair.

BPC (DM2)
2. Comply with specification: “completely closed” method.
3. Maintain present status: “cover on spot” method.

GC (DM3)
4. Relocate school site temporarily.
5. Don’t relocate school site.
6. Punish BPC.

Note: EPA: the Environmental Protection Agency; BPC: the Black Peony Company; GC: the Government
of Changzhou.

In the graph model of the Changzhou Conflict, there are 64 states in theory. However, some of the
states are logically infeasible; for instance, BPC cannot choose the two options of “completely closed”
method and “cover on spot” method simultaneously, nor can they choose neither option. Excluding
infeasible states, 12 types of feasible state ultimately remain, as listed in Table 3. For example, State 1
indicates that BPC chooses the “completely closed” method to purify the contaminated land, and GC
decides to relocate the school site temporarily.

Table 3. Feasible states of Changzhou conflict.

Decision Makers Options
Feasible States

1 2 3 4 5 6 7 8 9 10 11 12

EPA (DM1) Supervise N Y N Y N Y N Y N Y N Y

BPC (DM2)
“Completely closed” Y Y N N Y Y N N N N N N

“Cover on spot” N N Y Y N N Y Y Y Y Y Y

GC (DM3)
Relocate Y Y Y Y N N N N Y Y N N

Don’t relocate N N N N Y Y Y Y N N Y Y
Punish N N N N N N N N Y Y Y Y

Figures 2–4 exhibit the graph model of the Changzhou Conflict in terms of movement by EPA,
BPC, and GC, respectively.

Int. J. Environ. Res. Public Health 2017, 14, 1311 7 of 14

DMs and Options the—above‐mentioned Changzhou Conflict was mainly related to three DMs:

the Environmental Protection Agency (EPA), the Black Peony Company (BPC), and the Government

of Changzhou (GC). The options of each DM are listed in Table 2.

Table 2. DMs and options in the Changzhou conflict.

Decision Makers (DMs) Options

EPA (DM1) 1. Supervise the process of field repair.

BPC (DM2)
2. Comply with specification: “completely closed” method.

3. Maintain present status: “cover on spot” method.

GC (DM3)

4. Relocate school site temporarily.

5. Don’t relocate school site.

6. Punish BPC.

Note: EPA: the Environmental Protection Agency; BPC: the Black Peony Company; GC: the

Government of Changzhou.

In the graph model of the Changzhou Conflict, there are 64 states in theory. However, some of

the states are logically infeasible; for instance, BPC cannot choose the two options of “completely

closed” method and “cover on spot” method simultaneously, nor can they choose neither option.

Excluding infeasible states, 12 types of feasible state ultimately remain, as listed in Table 3. For

example, State 1 indicates that BPC chooses the “completely closed” method to purify the

contaminated land, and GC decides to relocate the school site

temporarily.

Table 3. Feasible states of Changzhou conflict.

Figures 2–4 exhibit the graph model of the Changzhou Conflict in terms of movement by EPA,

BPC, and GC, respectively.

Figure 2. Graph Model of Changzhou Conflict for Movement by EPA.

Figure 3. Graph Model of Changzhou Conflict for Movement by BPC.

Decision

Makers
Options

Feasible States

1 2 3 4 5 6 7 8 9 10 11 12

EPA (DM1) Supervise N Y N Y N Y N Y N Y N Y

BPC (DM2)
“Completely closed” Y Y N N Y Y N N N

N N N

“Cover on spot” N N Y Y N N Y Y Y Y Y Y

GC (DM3)

Relocate Y Y Y Y N N N N Y

Y N N

Don’t relocate N N N N Y Y Y Y N

N Y Y

Punish N N N N N N N N Y Y Y Y

Figure 2. Graph Model of Changzhou Conflict for Movement by EPA.

Int. J. Environ. Res. Public Health 2017, 14, 1311 8 of 15

Int. J. Environ. Res. Public Health 2017, 14, 1311 7 of 14

DMs and Options the—above‐mentioned Changzhou Conflict was mainly related to three DMs:
the Environmental Protection Agency (EPA), the Black Peony Company (BPC), and the Government
of Changzhou (GC). The options of each DM are listed in Table 2.
Table 2. DMs and options in the Changzhou conflict.
Decision Makers (DMs) Options
EPA (DM1) 1. Supervise the process of field repair.
BPC (DM2)
2. Comply with specification: “completely closed” method.
3. Maintain present status: “cover on spot” method.
GC (DM3)
4. Relocate school site temporarily.
5. Don’t relocate school site.
6. Punish BPC.
Note: EPA: the Environmental Protection Agency; BPC: the Black Peony Company; GC: the
Government of Changzhou.
In the graph model of the Changzhou Conflict, there are 64 states in theory. However, some of
the states are logically infeasible; for instance, BPC cannot choose the two options of “completely
closed” method and “cover on spot” method simultaneously, nor can they choose neither option.
Excluding infeasible states, 12 types of feasible state ultimately remain, as listed in Table 3. For
example, State 1 indicates that BPC chooses the “completely closed” method to purify the
contaminated land, and GC decides to relocate the school site temporarily.
Table 3. Feasible states of Changzhou conflict.
Figures 2–4 exhibit the graph model of the Changzhou Conflict in terms of movement by EPA,
BPC, and GC, respectively.

Figure 2. Graph Model of Changzhou Conflict for Movement by EPA.

Figure 3. Graph Model of Changzhou Conflict for Movement by BPC.

Decision
Makers
Options
Feasible States
1 2 3 4 5 6 7 8 9 10 11 12
EPA (DM1) Supervise N Y N Y N Y N Y N Y N Y
BPC (DM2)
“Completely closed” Y Y N N Y Y N N N N N N
“Cover on spot” N N Y Y N N Y Y Y Y Y Y
GC (DM3)
Relocate Y Y Y Y N N N N Y Y N N
Don’t relocate N N N N Y Y Y Y N N Y Y
Punish N N N N N N N N Y Y Y Y

Figure 3. Graph Model of Changzhou Conflict for Movement by BPC.Int. J. Environ. Res. Public Health 2017, 14, 1311 8 of 14

Figure 4. Graph Model of Changzhou Conflict for Movement by GC.

In this study, we use option prioritization to order the states; we get preference state sequences

according to preference statements. A positive number ( ) indicates that the DMs prefer the

preference statement; “ ” express that DMs hope it will not happen; “&” represents “and”, i.e., the

intersection of two options; “ ” represents “or”; IF means “if”…; and IFF signifies “if and only if”. A

term such as 6IF3 denotes “IF BPC remain with covering on spot, then EPA hopes that GC will punish

BPC”. The preference statements of EPA are represented vertically in Table 4 from the most preferred

to the least preferred. The EPA desires most that BPC will comply strictly with the operational

specifications. Their second preference is to monitor BPC as it purifies the contaminated land.

Table 4. Preference statements of EPA.

Interpretation Preference Statements

BPC complies with operational

specifications.
−3|2

Supervise the process of field repair. 1

If BPC retains coverage on the spot, then EPA

hopes that GC will punish BPC.
6IF3

If BPC retains coverage on spot, then EPA

hopes that GC will relocate school site

temporarily.

4IF3

Relocate school site temporarily. 4

DM1 (Environmental Protection Agency): P 2 6 1 5 10 12 4 8 9 11
3 7 . Based on the preference statements of EPA listed in Table 4, the decision support system
GMCRII gives out the preference state sequence of EPA. Among them, the left‐most‐ranked state

represents the DMs’ most preferred state, whereas the right‐most‐ranked state signifies the least

preferred state. For instance, EPA’s strongest preference is for BPC to adopt the “completely closed”

approach to purify the polluted soil, GC to decide to relocate the school site, and EPA itself to oversee

the practice of curing the polluted soil. The least‐preferred option is for BPC to choose the “cover on

spot” approach, that is, GC to punish the company and not move the school. Similarly, the preference

statements of BPC and GC are expressed in Tables 5 and 6, respectively, and the corresponding

preference state sequences are as given by GMCR II.

DM2 (Black Peony Company): P 3 7 4 8 1 5 2 6 9 11 10 12 . DM3
(The Government of Changzhou): P 6 2 5 1 12 10 8 4 11 9 7 3 .

Table 5. Preference statements of BPC.

Interpretation Preference Statements

Don’t want to be penalized by GC. −6

Continue choosing “cover on spot” method. 3

Don’t want EPA to be involved. −1

Relocate school site temporarily. 4




Figure 4. Graph Model of Changzhou Conflict for Movement by GC.

In this study, we use option prioritization to order the states; we get preference state sequences
according to preference statements. A positive number (+) indicates that the DMs prefer the preference
statement; “—” express that DMs hope it will not happen; “&” represents “and”, i.e., the intersection
of two options; “|” represents “or”; IF means “if” . . . ; and IFF signifies “if and only if”. A term such
as 6IF3 denotes “IF BPC remain with covering on spot, then EPA hopes that GC will punish BPC”.
The preference statements of EPA are represented vertically in Table 4 from the most preferred to the
least preferred. The EPA desires most that BPC will comply strictly with the operational specifications.
Their second preference is to monitor BPC as it purifies the contaminated land.

Table 4. Preference statements of EPA.

Interpretation Preference Statements

BPC complies with operational specifications. −3|2
Supervise the process of field repair. 1

If BPC retains coverage on the spot, then EPA hopes
that GC will punish BPC.

6IF3

If BPC retains coverage on spot, then EPA hopes that
GC will relocate school site temporarily.

4IF3

Relocate school site temporarily. 4

DM1 (Environmental Protection Agency): P = [2 > 6 > 1 > 5 > 10 > 12 > 4 > 8 > 9 > 11 > 3 > 7].
Based on the preference statements of EPA listed in Table 4, the decision support system GMCRII
gives out the preference state sequence of EPA. Among them, the left-most-ranked state represents
the DMs’ most preferred state, whereas the right-most-ranked state signifies the least preferred state.
For instance, EPA’s strongest preference is for BPC to adopt the “completely closed” approach to purify
the polluted soil, GC to decide to relocate the school site, and EPA itself to oversee the practice of
curing the polluted soil. The least-preferred option is for BPC to choose the “cover on spot” approach,
that is, GC to punish the company and not move the school. Similarly, the preference statements of
BPC and GC are expressed in Tables 5 and 6, respectively, and the corresponding preference state
sequences are as given by GMCR II.

DM2 (Black Peony Company): P = [3 > 7 > 4 > 8 > 1 > 5 > 2 > 6 > 9 > 11 > 10 > 12]. DM3
(The Government of Changzhou): P = [6 > 2 > 5 > 1 > 12 > 10 > 8 > 4 > 11 > 9 > 7 > 3].

Table 5. Preference statements of BPC.

Interpretation Preference Statements

Don’t want to be penalized by GC. −6
Continue choosing “cover on spot” method. 3

Don’t want EPA to be involved. −1
Relocate school site temporarily. 4

Int. J. Environ. Res. Public Health 2017, 14, 1311 9 of 15

Table 6. Preference Statements of GC.

Interpretation Preference statements

Hope BPC complies with specifications. −3|2
EPA supervises the process. 1

If EPA supervises while BPC continues covering on spot, then GC will penalize BPC. 6IF(1 and 3)
Don’t relocate school site. 5

Next, we consider the preference state sequences provided by the means of developed option

prioritization. In this case, g = 2; α = 12 , and α
t =

(
1
2

)t
. Table 7 shows the three DMs’ levels of

confidence in their judgments.

Table 7. C of Preference Statements of DM1, DM2 and DM3.

Serial Number of Preference Statement DM1 C1 DM2 C2 DM3 C3

p = 3

1
p = 3
1

p = 4

2 1 1 1

3 1 1 1

4 4/9 1/4 1

5 1/9

Each state score for an individual DM can be calculated on the basis of the score function discussed
above, and is displayed in Tables 8–10.

Table 8. SC of EPA.

Decision Maker
State 1 2 3 4 5 6

SC 0.50347 0.75347 0.02778 0.25010 0.50000 0.75000

DM1
State 7 8 9 10 11 12

SC 0.00000 0.25000 0.15625 0.40625 0.12500 0.37500

Table 9. SC of BPC.

Decision Maker
State 1 2 3 4 5 6

SC 0.64063 0.51563 0.89063 0.76563 0.62500 0.50000

DM2
State 7 8 9 10 11 12

SC 0.87500 0.75000 0.39063 0.26563 0.37500 0.25000

Table 10. SC of GC.

Decision Maker
State 1 2 3 4 5 6

SC 0.50000 0.75000 0.00000 0.25000 0.56250 0.81250

DM3
State 7 8 9 10 11 12

SC 0.06250 0.31250 0.12500 0.37500 0.18750 0.43750

The ranked states according to SC for all DMs are summarized as follows:

P(DM1) = [2 > 6 > 1 > 5 > 10 > 12 > 4 > 8 > 9 > 11 > 3 > 7];

P(DM2) = [3 > 7 > 4 > 8 > 1 > 5 > 2 > 6 > 9 > 11 > 10 > 12];

P(DM3) = [6 > 2 > 5 > 1 > 12 > 10 > 8 > 4 > 11 > 9 > 7 > 3];

The new preference state sequences are consistent with the original results that relied on
option prioritization.

Int. J. Environ. Res. Public Health 2017, 14, 1311 10 of 15

4.2. Stability Analysis

According to the definitions of the four stabilities, the equilibrium states can be drawn as shown
in Table 11, in which indicates that the state is an equilibrium state corresponding to the respective
stability definition.

Table 11. Equilibrium states of the Changzhou conflict.

Stability
Equilibrium States

1 2 5 6 12

Nash

Int. J. Environ. Res. Public Health 2017, 14, 1311 10 of 14

4.2. Stability Analysis

According to the definitions of the four stabilities, the equilibrium states can be drawn as shown
in Table 11, in which √ indicates that the state is an equilibrium state corresponding to the respective
stability definition.

Table 11. Equilibrium states of the Changzhou conflict.

Stability Equilibrium States
1 2 5 6 12

Nash 

GMR     
SMR     
SEQ     

GMR: general meta-rationality; SMR: symmetric meta-rationality; SEQ: sequential stability.

For Nash stability, the equilibrium state is State 12. For GMR, SMR, and SEQ stabilities, the
equilibrium states are 1, 2, 5, 6, and 12. State 12 is a strong equilibrium, but it cannot fundamentally
resolve the conflict. State 12 implies that EPA is involved in and supervises BPC, but BPC still chooses
the “cover on spot” approach to purify the soil, which not only cannot cure the environmental
problem but is also a hazard to the health of the teachers and students. Based on these, GC penalizes
BPC and relocates the school site. This is obviously a far-from-ideal solution to solving the
Changzhou Conflict. State 6 indicates that under the supervision of EPA, BPC adopts the “completely
closed” means of purifying the contaminated land, which would reduce the impact of volatile
pollutants on teachers and students. Under the premise of effectively protecting the health of students
and teachers, GC does not relocate the school site, and this state would effectively coordinate the
interests of all DMs. State 2 shows EPA being involved in overseeing the company’s purification
course and BPC choosing the “completely closed” method, while GC still decides to relocate the
school site. Comparing States 2 and 6, the latter is a better solution based on the consideration of
social and economic benefits.

In the case of the Changzhou Conflict discussed above, Figure 5 describes the path of the conflict
from the status quo through an intermediate state to the final resolution. After BPC purifies the soil
by fully enclosing the site, GC decides not to move the Changzhou Foreign Language School (move
from State 1 to State 5). In order to actually protect the teachers and students, and to prevent a similar
accident from happening again, EPA decides to supervise BPC. This state not only achieves the
resolution of healing the environment properly, but also diminishes the physical harm to teachers
and students. At this point, each participant in the Changzhou Conflict reaches a balanced state.

Decision Makers

Status Quo
State

Intermediate
State

Equilibrium
State

1 5 6

EPA (DM1) N N Y

BPC (DM2)
Y Y Y

N N N

GC (DM3)

Y N N

N Y Y

N N N

Figure 5. Evolution of the conflict from the status quo through an intermediate state to the final
resolution.

GMR

Int. J. Environ. Res. Public Health 2017, 14, 1311 10 of 14

Nash 
GMR     
SMR     
SEQ     

GMR: general meta-rationality; SMR: symmetric meta-rationality; SEQ: sequential stability.
For Nash stability, the equilibrium state is State 12. For GMR, SMR, and SEQ stabilities, the
equilibrium states are 1, 2, 5, 6, and 12. State 12 is a strong equilibrium, but it cannot fundamentally
resolve the conflict. State 12 implies that EPA is involved in and supervises BPC, but BPC still chooses
the “cover on spot” approach to purify the soil, which not only cannot cure the environmental
problem but is also a hazard to the health of the teachers and students. Based on these, GC penalizes
BPC and relocates the school site. This is obviously a far-from-ideal solution to solving the
Changzhou Conflict. State 6 indicates that under the supervision of EPA, BPC adopts the “completely
closed” means of purifying the contaminated land, which would reduce the impact of volatile
pollutants on teachers and students. Under the premise of effectively protecting the health of students
and teachers, GC does not relocate the school site, and this state would effectively coordinate the
interests of all DMs. State 2 shows EPA being involved in overseeing the company’s purification
course and BPC choosing the “completely closed” method, while GC still decides to relocate the
school site. Comparing States 2 and 6, the latter is a better solution based on the consideration of
social and economic benefits.
In the case of the Changzhou Conflict discussed above, Figure 5 describes the path of the conflict
from the status quo through an intermediate state to the final resolution. After BPC purifies the soil
by fully enclosing the site, GC decides not to move the Changzhou Foreign Language School (move
from State 1 to State 5). In order to actually protect the teachers and students, and to prevent a similar
accident from happening again, EPA decides to supervise BPC. This state not only achieves the
resolution of healing the environment properly, but also diminishes the physical harm to teachers
and students. At this point, each participant in the Changzhou Conflict reaches a balanced state.
Decision Makers
Status Quo
State
Intermediate
State
Equilibrium
State
1 5 6
EPA (DM1) N N Y
BPC (DM2)
Y Y Y
N N N
GC (DM3)
Y N N
N Y Y
N N N
Figure 5. Evolution of the conflict from the status quo through an intermediate state to the final
resolution.

Int. J. Environ. Res. Public Health 2017, 14, 1311 10 of 14

4.2. Stability Analysis
According to the definitions of the four stabilities, the equilibrium states can be drawn as shown
in Table 11, in which √ indicates that the state is an equilibrium state corresponding to the respective
stability definition.
Table 11. Equilibrium states of the Changzhou conflict.
Stability Equilibrium States
1 2 5 6 12
Nash 
GMR     
SMR     
SEQ     
GMR: general meta-rationality; SMR: symmetric meta-rationality; SEQ: sequential stability.
For Nash stability, the equilibrium state is State 12. For GMR, SMR, and SEQ stabilities, the
equilibrium states are 1, 2, 5, 6, and 12. State 12 is a strong equilibrium, but it cannot fundamentally
resolve the conflict. State 12 implies that EPA is involved in and supervises BPC, but BPC still chooses
the “cover on spot” approach to purify the soil, which not only cannot cure the environmental
problem but is also a hazard to the health of the teachers and students. Based on these, GC penalizes
BPC and relocates the school site. This is obviously a far-from-ideal solution to solving the
Changzhou Conflict. State 6 indicates that under the supervision of EPA, BPC adopts the “completely
closed” means of purifying the contaminated land, which would reduce the impact of volatile
pollutants on teachers and students. Under the premise of effectively protecting the health of students
and teachers, GC does not relocate the school site, and this state would effectively coordinate the
interests of all DMs. State 2 shows EPA being involved in overseeing the company’s purification
course and BPC choosing the “completely closed” method, while GC still decides to relocate the
school site. Comparing States 2 and 6, the latter is a better solution based on the consideration of
social and economic benefits.
In the case of the Changzhou Conflict discussed above, Figure 5 describes the path of the conflict
from the status quo through an intermediate state to the final resolution. After BPC purifies the soil
by fully enclosing the site, GC decides not to move the Changzhou Foreign Language School (move
from State 1 to State 5). In order to actually protect the teachers and students, and to prevent a similar
accident from happening again, EPA decides to supervise BPC. This state not only achieves the
resolution of healing the environment properly, but also diminishes the physical harm to teachers
and students. At this point, each participant in the Changzhou Conflict reaches a balanced state.
Decision Makers
Status Quo
State
Intermediate
State
Equilibrium
State
1 5 6
EPA (DM1) N N Y
BPC (DM2)
Y Y Y
N N N
GC (DM3)
Y N N
N Y Y
N N N
Figure 5. Evolution of the conflict from the status quo through an intermediate state to the final
resolution.

Int. J. Environ. Res. Public Health 2017, 14, 1311 10 of 14

SMR

Int. J. Environ. Res. Public Health 2017, 14, 1311 10 of 14

SEQ

Int. J. Environ. Res. Public Health 2017, 14, 1311 10 of 14

GMR: general meta-rationality; SMR: symmetric meta-rationality; SEQ: sequential stability.

For Nash stability, the equilibrium state is State 12. For GMR, SMR, and SEQ stabilities,
the equilibrium states are 1, 2, 5, 6, and 12. State 12 is a strong equilibrium, but it cannot fundamentally
resolve the conflict. State 12 implies that EPA is involved in and supervises BPC, but BPC still chooses
the “cover on spot” approach to purify the soil, which not only cannot cure the environmental problem
but is also a hazard to the health of the teachers and students. Based on these, GC penalizes BPC and
relocates the school site. This is obviously a far-from-ideal solution to solving the Changzhou Conflict.
State 6 indicates that under the supervision of EPA, BPC adopts the “completely closed” means of
purifying the contaminated land, which would reduce the impact of volatile pollutants on teachers
and students. Under the premise of effectively protecting the health of students and teachers, GC does
not relocate the school site, and this state would effectively coordinate the interests of all DMs. State 2
shows EPA being involved in overseeing the company’s purification course and BPC choosing the
“completely closed” method, while GC still decides to relocate the school site. Comparing States 2
and 6, the latter is a better solution based on the consideration of social and economic benefits.

In the case of the Changzhou Conflict discussed above, Figure 5 describes the path of the conflict
from the status quo through an intermediate state to the final resolution. After BPC purifies the
soil by fully enclosing the site, GC decides not to move the Changzhou Foreign Language School
(move from State 1 to State 5). In order to actually protect the teachers and students, and to prevent a
similar accident from happening again, EPA decides to supervise BPC. This state not only achieves the
resolution of healing the environment properly, but also diminishes the physical harm to teachers and
students. At this point, each participant in the Changzhou Conflict reaches a balanced state.

Int. J. Environ. Res. Public Health 2017, 14, 1311 10 of 14

4.2. Stability Analysis

According to the definitions of the four stabilities, the equilibrium states can be drawn as shown

in Table 11, in which √ indicates that the state is an equilibrium state corresponding to the respective

stability definition.

Table 11. Equilibrium states of the Changzhou conflict.

Stability
Equilibrium States

1 2 5 6 12

Nash 

GMR     

SMR     

SEQ     

GMR: general meta‐rationality; SMR: symmetric meta‐rationality; SEQ: sequential stability.

For Nash stability, the equilibrium state is State 12. For GMR, SMR, and SEQ stabilities, the

equilibrium states are 1, 2, 5, 6, and 12. State 12 is a strong equilibrium, but it cannot fundamentally

resolve the conflict. State 12 implies that EPA is involved in and supervises BPC, but BPC still chooses

the “cover on spot” approach to purify the soil, which not only cannot cure the environmental

problem but is also a hazard to the health of the teachers and students. Based on these, GC penalizes

BPC and relocates the school site. This is obviously a far‐from‐ideal solution to solving the

Changzhou Conflict. State 6 indicates that under the supervision of EPA, BPC adopts the “completely

closed” means of purifying the contaminated land, which would reduce the impact of volatile

pollutants on teachers and students. Under the premise of effectively protecting the health of students

and teachers, GC does not relocate the school site, and this state would effectively coordinate the

interests of all DMs. State 2 shows EPA being involved in overseeing the company’s purification

course and BPC choosing the “completely closed” method, while GC still decides to relocate the

school site. Comparing States 2 and 6, the latter is a better solution based on the consideration of

social and economic benefits.

In the case of the Changzhou Conflict discussed above, Figure 5 describes the path of the conflict

from the status quo through an intermediate state to the final resolution. After BPC purifies the soil

by fully enclosing the site, GC decides not to move the Changzhou Foreign Language School (move

from State 1 to State 5). In order to actually protect the teachers and students, and to prevent a similar

accident from happening again, EPA decides to supervise BPC. This state not only achieves the

resolution of healing the environment properly, but also diminishes the physical harm to teachers

and students. At this point, each participant in the Changzhou Conflict reaches a balanced state.

Decision Makers

Status Quo

State

Intermediate

State

Equilibrium

State

1 5 6

EPA (DM1) N N Y

BPC (DM2)
Y Y Y

N N N
GC (DM3)
Y N N
N Y Y
N N N

Figure 5. Evolution of the conflict from the status quo through an intermediate state to the final

resolution.

Figure 5. Evolution of the conflict from the status quo through an intermediate state to the
final resolution.

Int. J. Environ. Res. Public Health 2017, 14, 1311 11 of 15

4.3. Coalition Analysis

Comparing Tables 11 and 12, we find the following: States 1 and 5 are balanced, but while the DMs
consider a coalition, States 1 and 5 are not in equilibrium. Now, suppose that there are equilibrium
jumps after the DMs reach a coalition. Figure 6 draws the path of an equilibrium jump from State 1 to
State 6. The GC contracts an alliance with EPA: with the support of GC, EPA takes action to supervise
BPC, binding upon it. On this occasion, having effectively protected the health of the teachers and
students, GC decides not to relocate the school site on the basis of the social and economic benefits.
In other words, there is a direct transfer from State 1 to State 6.

Table 12. Coalition equilibrium states of Changzhou conflict.

Stability
Coalition Equilibrium States

2 6 12

Nash
Int. J. Environ. Res. Public Health 2017, 14, 1311 10 of 14

GMR
Int. J. Environ. Res. Public Health 2017, 14, 1311 10 of 14

Int. J. Environ. Res. Public Health 2017, 14, 1311 10 of 14

SMR
Int. J. Environ. Res. Public Health 2017, 14, 1311 10 of 14

Int. J. Environ. Res. Public Health 2017, 14, 1311 10 of 14

SEQ
Int. J. Environ. Res. Public Health 2017, 14, 1311 10 of 14

Int. J. Environ. Res. Public Health 2017, 14, 1311 10 of 14

The main reasons for coalition as far as GC and EPA are concerned are that State 6 is better than
State 1 for both coalition participants, and neither can get to State 6 by unilateral improvement. From a
practical point of view, it is very common for government offices to partner in the case of an emergency.

Int. J. Environ. Res. Public Health 2017, 14, 1311 11 of 14

4.3. Coalition Analysis

Comparing Tables 11 and 12, we find the following: States 1 and 5 are balanced, but while the

DMs consider a coalition, States 1 and 5 are not in equilibrium. Now, suppose that there are

equilibrium jumps after the DMs reach a coalition. Figure 6 draws the path of an equilibrium jump

from State 1 to State 6. The GC contracts an alliance with EPA: with the support of GC, EPA takes

action to supervise BPC, binding upon it. On this occasion, having effectively protected the health of

the teachers and students, GC decides not to relocate the school site on the basis of the social and

economic benefits. In other words, there is a direct transfer from State 1 to State 6.

Table 12. Coalition equilibrium states of Changzhou conflict.

Stability
Coalition Equilibrium States

2 6 12

Nash 

GMR   

SMR   

SEQ   

The main reasons for coalition as far as GC and EPA are concerned are that State 6 is better than

State 1 for both coalition participants, and neither can get to State 6 by unilateral improvement. From

a practical point of view, it is very common for government offices to partner in the case of an

emergency.

Figure 6. Evolution of Changzhou Conflict from the Status Quo to the Final Resolution.

4.4. Coalition Motivation and Real‐Coalition Stability Analysis

In line with the values of or EPA and GC, we establish the appropriate score coordinate

system as depicted in Figures 7 and 8.

Figure 6. Evolution of Changzhou Conflict from the Status Quo to the Final Resolution.

4.4. Coalition Motivation and Real-Coalition Stability Analysis

In line with the values of SC or EPA and GC, we establish the appropriate score coordinate system
as depicted in Figures 7 and 8.

C I(H1) = 7.205. Because C I > 1, we say that the state improved significantly with a coalition
between GC and EPA. As shown in Figure 7, points SC2 and SC3 are relatively close together. The SC
of the coalition equilibrium state is closer to the SC of the most preferred state.

C I(H2) = +∞; hence, the coalition equilibrium state is the most preferred state, which is the best
result for a coalition. After coalition, the states of EPA and GC improve significantly, but the level of
improvement for GC is evidently better than that for EPA. So, as the coalition progresses, GC will
be more motivated to promote the coalition and devote itself to contribute to it. The values of C I
for both coalition DMs are greater than 1, i.e., C I(H1) > 1 and C I(H2) > 1. This implies that both
parties would find it easy to reach a consensus in the course of the coalition. The coalition relationship
would be noticeably solid, and the coalition status would not be disturbed by exterior circumstances.
In reality, coalitions between government departments tend to be exceedingly tight, so this finding is
more consistent with real life.

Int. J. Environ. Res. Public Health 2017, 14, 1311 12 of 15

Int. J. Environ. Res. Public Health 2017, 14, 1311 12 of 14

Figure 7. Score coordinate system of EPA (DM1).

7.205. Because 1, we say that the state improved significantly with a coalition
between GC and EPA. As shown in Figure 7, points and are relatively close together. The
of the coalition equilibrium state is closer to the of the most preferred state.

Figure 8. Score Coordinate System of GC (DM3).

∞; hence, the coalition equilibrium state is the most preferred state, which is the best
result for a coalition. After coalition, the states of EPA and GC improve significantly, but the level of

improvement for GC is evidently better than that for EPA. So, as the coalition progresses, GC will be

more motivated to promote the coalition and devote itself to contribute to it. The values of for
both coalition DMs are greater than 1, i.e., 1 and 1 . This implies that both parties
would find it easy to reach a consensus in the course of the coalition. The coalition relationship would

be noticeably solid, and the coalition status would not be disturbed by exterior circumstances. In

reality, coalitions between government departments tend to be exceedingly tight, so this finding is

more consistent with real life.

Figure 7. Score coordinate system of EPA (DM1).

Int. J. Environ. Res. Public Health 2017, 14, 1311 12 of 14

Figure 7. Score coordinate system of EPA (DM1).
7.205. Because 1, we say that the state improved significantly with a coalition
between GC and EPA. As shown in Figure 7, points and are relatively close together. The
of the coalition equilibrium state is closer to the of the most preferred state.

Figure 8. Score Coordinate System of GC (DM3).
∞; hence, the coalition equilibrium state is the most preferred state, which is the best
result for a coalition. After coalition, the states of EPA and GC improve significantly, but the level of
improvement for GC is evidently better than that for EPA. So, as the coalition progresses, GC will be
more motivated to promote the coalition and devote itself to contribute to it. The values of for
both coalition DMs are greater than 1, i.e., 1 and 1 . This implies that both parties
would find it easy to reach a consensus in the course of the coalition. The coalition relationship would
be noticeably solid, and the coalition status would not be disturbed by exterior circumstances. In
reality, coalitions between government departments tend to be exceedingly tight, so this finding is
more consistent with real life.

Figure 8. Score Coordinate System of GC (DM3).

5. Conclusions

Having considered the difference in the state preferences of DMs, we proposed a confidence level
function, αt, and a Boolean function about preference statements as a foundation on which to construct
a score function We then proposed a paradigm for measuring the coalition motivation of each DM,
and further studied real-coalition stability. Finally, we applied an improved GMCR to the Changzhou
Conflict, contrasting the original and new methods to find that the new preference state sequences were
consistent with the original results. Through real-coalition stability analysis, we found the following:
The Government of Changzhou would be more autonomous and would commit itself to coalition, and

Int. J. Environ. Res. Public Health 2017, 14, 1311 13 of 15

an alliance with the EPA would not be interrupted by external factors or other outsiders, meaning
that the coalition relationship would not be easily broken up. Future research could be expanded
from the following two aspects: (1) identify the main contradiction through sensitivity analysis to
more effectively address the problem or guide the evolution of a conflict toward an expected direction;
and (2) accurately measure the impact of opportunity cost on coalition results in the real world by a
quantitative method.

Acknowledgments: The National Social Science Fund Major Projects (14ZDB151) and Key Projects (16AZD018);
National Science Foundation of China under Grants (41701593, 71371098, 71571157); National Key Research
and Development Program of China (2016YFC1402000); Public Welfare Industry Research Projects (201305034,
201405029); The Ministry of Education Philosophy and Social Sciences Development Report Breeding Project
(13JBGP005); General Financial Grant from the China Postdoctoral Science Foundation (2015M580611); Qingdao
Postdoctoral Application Research Project Funding (251); Fundamental Research Funds for the Central Universities
(201613006, 201564031).

Author Contributions: Kedong Yin designed the structure and analyzed the case study; Xuemei Li proposed the
idea; Li Yu wrote the paper and perform the calculations.

Conflicts of Interest: The authors declare no conflict of interest.

References

1. Fraser, N.M.; Hipel, K.W. Solving complex conflicts. IEEE Trans. Syst. Man Cybern. 1979, 9, 805–816.
[CrossRef]

2. Fraser, N.M.; Hipel, K.W. Conflict Analysis: Models and Resolutions; Elsevier Science Ltd.: Toronto, ON,
Canada, 1984.

3. Kilgour, D.M.; Hipel, K.W.; Fang, L.-P. The graph model for conflict. Automatica 1987, 23, 41–55. [CrossRef]
4. Walker, S.B.; Hipel, K.W.; Inohara, T. Dominating attitudes in the graph model for conflict resolution. J. Syst.

Sci. Syst. Eng. 2012, 21, 316–336. [CrossRef]
5. Obeidi, A.; Hipel, K.W.; Kilgour, D.M. The role of emotions in envisioning outcomes in conflict analysis.

Group Decis. Negot. 2005, 14, 481–500. [CrossRef]
6. Al-Mutairi, M.S.; Hipel, K.W.; Kamel, M.S. Fuzzy preferences in conflicts. J. Syst. Sci. Syst. Eng. 2008, 17,

257–276. [CrossRef]
7. Peng, X.; Hipel, K.W.; Kilgour, D.M.; Fang, L.-P. Representing ordinal preferences in the decision support

system GMCR II. Int. Conf. IEEE 1997, 1, 809–814.
8. Bashar, M.A.; Kilgour, D.M.; Hipel, K.W. Fuzzy truth values in option prioritization for preference elicitation

in the graph mode. In Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics
(SMC), Seoul, Korea, 14–17 October 2012; pp. 3081–3086.

9. Yu, J.; Yu, Q. A conflict analysis framework considering fuzzy preferences. J. Intell. Fuzzy Syst. 2015, 29,
2743–2749. [CrossRef]

10. Kuang, H.; Bashar, M.A.; Hipel, K.W.; Kilgour, D.M. Grey-based preference in a Graph Model for Conflict
Resolution with multiple decision makers. IEEE Trans. Syst. Man Cybern. Syst. 2015, 45, 1254–1267.
[CrossRef]

11. Yang, F.; Guan, Y. Graph model for conflict resolution analysis based on interval grey number preference.
In Proceedings of the IEEE International Conference on Grey Systems and Intelligent Services (GSIS),
Leicester, UK, 18–20 August 2015; pp. 49–53.

12. Liu, Y. Graph Model for Conflict Resolution with Grey Information and Application. In Proceedings
of the IEEE International Conference on Grey Systems and Intelligent Services (GSIS), Leicester, UK,
18–20 August 2015; pp. 54–60.

13. Hamouda, L.; Kilgour, D.M.; Hipel, K.W. Strength of preference in graph models for multiple-decision-maker
conflicts. Appl. Math. Comput. 2006, 179, 314–327. [CrossRef]

14. Li, K.W.; Hipel, K.W.; Kilgour, D.M.; Noakes, D. Integrating uncertain preferences into status quo analysis
with applications to an environmental conflict. Group Decis. Negot. 2005, 14, 461–479. [CrossRef]

15. Yu, J.; Hipel, K.W.; Kilgour, D.M.; Zhao, M. Option prioritization for unknown preference. J. Syst. Sci.
Syst. Eng. 2016, 25, 39–61. [CrossRef]

http://dx.doi.org/10.1109/TSMC.1979.4310131

http://dx.doi.org/10.1016/0005-1098(87)90117-8

http://dx.doi.org/10.1007/s11518-012-5198-x

http://dx.doi.org/10.1007/s10726-005-9004-8

http://dx.doi.org/10.1007/s11518-008-5088-4

http://dx.doi.org/10.3233/IFS-151978

http://dx.doi.org/10.1109/TSMC.2014.2387096

http://dx.doi.org/10.1016/j.amc.2005.11.109

http://dx.doi.org/10.1007/s10726-005-9003-9

http://dx.doi.org/10.1007/s11518-015-5282-0

Int. J. Environ. Res. Public Health 2017, 14, 1311 14 of 15

16. Kilgour, D.M.; Hipel, K.W.; Fang, L.-P.; Peng, X. Coalition analysis in group decision support.
Group Decis. Negot. 2001, 10, 159–175. [CrossRef]

17. Kinsara, R.A.; Kilgour, D.M.; Hipel, K.W. Inverse approach to the graph model for conflict resolution.
IEEE Trans. Syst. Man Cybern. Syst. 2015, 45, 734–742. [CrossRef]

18. Kinsara, R.A.; Hipel, K.W.; Kilgour, D.M. New Approaches to Understanding Conflict Resolution Results.
In Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics, Kowloon, China,
9–12 October 2015; pp. 623–628.

19. Hipel, K.W.; Kilgour, D.M.; Fang, L.-P.; Peng, X. The decision support system GMCR II in negotiations over
groundwater contamination. Syst. Man Cybern. 1999, 5, 942–948.

20. Karnis, M.; Bristow, M.; Fang, L.-P. Controversy over the international upper great lakes study
recommendations: Pathways towards cooperation. In Proceedings of the International Conference on
Group Decision and Negotiation, Warsaw, Poland, 22–26 June 2015; pp. 255–267.

21. Huang, J.-H.; Liu, G.-S. MGMCR and Its Application to Negotiation Support Systems. Syst. Eng. Theory Pract.
2002, 2, 68–72.

22. Wang, Q.; Kilgour, D.M.; Hipel, K.W. Facilitating risky project negotiation: An integrated approach using
fuzzy real options, multicriteria analysis, and conflict analysis. Inf. Sci. 2015, 295, 544–557. [CrossRef]

23. Kuang, H.; Bashar, M.A.; Kilgour, D.M.; Hipel, K.W. Strategic analysis of a brownfield revitalization conflict
using the grey-based graph model for conflict resolution. EURO J. Decis. Processes 2015, 3, 219–248. [CrossRef]

24. Han, X.-S.; Xu, H.-Y.; Liao, C.H.; Wang, Q.-Q. Research of the Process Conflict for Complex Product Based on
Graph Model. Mod. Manag. 2012, 2, 39–44. [CrossRef]

25. Chu, Y.; Hipel, K.W.; Fang, L.-P.; Wang, H. Systems methodology for resolving water conflicts: The Zhanghe
River water allocation dispute in China. Int. J. Water Resour. Dev. 2015, 31, 106–119. [CrossRef]

26. Li, J.; Han, W.; Xu, H. Credit expansion and concentration in China based on GMCR. In Proceedings
of the IEEE International Conference on Grey Systems and Intelligent Services (GSIS), Leicester, UK,
18–20 August 2015; pp. 635–639.

27. Bashar, M.A.; Kilgour, D.M.; Hipel, K.W. Fuzzy option prioritization for the graph model for conflict
resolution. Fuzzy Sets Syst. 2014, 246, 34–48. [CrossRef]

28. Bashar, M.A.; Obeidi, A.; Kilgour, M. Modeling Fuzzy and Interval Fuzzy Preferences within a Graph Model
Framework. IEEE Trans. Fuzzy Syst. 2016, 24, 765–778. [CrossRef]

29. Bashar, M.A.; Hipel, K.W.; Kilgour, D.M.; Obeidi, A. Coalition fuzzy stability analysis in the Graph Model
for Conflict Resolution. J. Intell. Fuzzy Syst. 2015, 29, 593–607. [CrossRef]

30. Hipel, K.W.; Kilgour, D.M.; Bashar, M.A. Fuzzy preferences in multiple participant decision making. Sci. Iran.
2011, 18, 627–638. [CrossRef]

31. Bashar, M.A.; Kilgour, D.M.; Hipel, K.W. Fuzzy preferences in the graph model for conflict resolution.
IEEE Trans. Fuzzy Syst. 2012, 20, 760–770. [CrossRef]

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
(CC BY) license (http://creativecommons.org/licenses/by/4.0/).

http://dx.doi.org/10.1023/A:1008713120075

http://dx.doi.org/10.1109/TSMC.2014.2376473

http://dx.doi.org/10.1016/j.ins.2014.10.049

http://dx.doi.org/10.1007/s40070-015-0042-4

http://dx.doi.org/10.12677/mm.2012.21008

http://dx.doi.org/10.1080/07900627.2014.933096

http://dx.doi.org/10.1016/j.fss.2014.02.011

http://dx.doi.org/10.1109/TFUZZ.2015.2446536

http://dx.doi.org/10.3233/IFS-141336

http://dx.doi.org/10.1016/j.scient.2011.04.016

http://dx.doi.org/10.1109/TFUZZ.2012.2183603

Homepage

http://creativecommons.org/licenses/by/4.0/.

Reproduced with permission of copyright owner. Further reproduction
prohibited without permission.

Introduction and Motivation
Framework of Graph Model for Conflict Resolution
Score Function and Real-Coalition Analysis

Score Function
Real-Coalition Analysis with Two DMs

Application of Improved GMCR

Background of Conflict and Modeling
Stability Analysis
Coalition Analysis
Coalition Motivation and Real-Coalition Stability Analysis
Conclusions

Conflict analysis based on the
graph model for conflict

resolution and grey matrix
Xueshan Han, Thi Dieu Linh Nguyen and Haiyan Xu

College of Economics and Management,
Nanjing University of Aeronautics and Astronautics, Nanjing, China

Abstract

Purpose – The purpose of this paper is to propose a complete theory of grey conflict analysis model
based on grey game and the graph model for conflict resolution and also, to illustrate a case of
“prisoner’s dilemma” in the traditional grey game as an example.

Design/methodology/approach – Based on the theories of grey game and graph model for conflict
resolution, this paper concentrates on the model of grey conflict analysis in a case of two players under
the condition of symmetrical loss information. By analyzing decision makers, strategies, states, graph
model and grey potential, and the number of decision makers’ steps, the pure strategy Nash equilibrium
is extended to grey potential-general metarationality, grey potential-symmetrical metarationality, and
grey potential-sequential stability. Meanwhile, the logical relationships between solutions are
discussed. A specific case study is carried out to illustrate how the proposed grey conflict analysis model
is used in practice.

Findings – The results in this paper indicate that more stable solutions are found when one consider

the grey potential-general metarationality, the grey potential-symmetrical metarationality, and the
grey potential-sequential stability, and then solve the paradox of “prisoner’s dilemma”.

Practical implications – This new grey conflict analysis model could be used to provide useful
information for policy makers during existing conflicts or negotiations among parties or enterprises.

Originality/value – The paper succeeds in constructing a new grey conflict analysis model, in which the
solution concepts are studied; and the two-player grey game will be extended to n-players in the near future.

Keywords Grey systems, Conflict resolution, Game theory, Conflict analysis, Grey game, Grey potential,
Pure strategy,

Equilibrium

Paper type Research paper

1. Introduction
The classical game theory ( John and Osakar, 1944) was built on the precise mathematical
fundamental. However, sometimes it cannot be used in practice due to the requirement for
complete information. For example, in the zero-sum games of two-players, the profit and
loss matrix that two game players depend on is from the judgment information. Due to the
cognitive level, incomplete information, grey information (Deng, 1

2) and the uncertainty
of the future, game players may not have significant understanding for their strategic
characteristics, space and payoff function, even if the information involved parties are
symmetrical. Many researches are focusing their study on the game containing incomplete
information. For example, Professor Fang and Liu (2003a, b, c) proposed the grey matrix
game model based on pure strategy. Sequentially, Fang and Liu (2006) developed the
matrix game of grey situation-pure-tactical Nash equilibrium in symmetrical loss
information of game-equilibrium in n-people. They applied the ideology and theory of grey
system to establish the standard grey matrix game and thus result in non-classical grey

The current issue and full text archive of this journal is available at

www.emeraldinsight.com/2043-9377.htm

Conflict analysis

Grey Systems: Theory and
Application

Vol. 3 No. 1, 2013
pp. 95-

106

q Emerald Group Publishing Limited
2043-9377

DOI 10.1108/20439371311293723

number areas. Based on the zero-sum finite games of two-players and the most
conservative game decision problem, Fang et al. proposed the necessary and sufficient
conditions, as well as mentioned the concept of grey saddle point. Tao et al. (2004)
introduced the definition of grey saddle point of grey mixed strategy based on mixed
strategy of the grey matrix games. Also working on grey matrix and grey matrix game
theory, Luo and Wu (2005) proposed the upper and lower equilibrium solution, ideal
equilibrium solution, u positioned equilibrium solution and average positioned
equilibrium solution. Luo and Wu (2006) focused on the concept of equilibrium solution
and then established a method to rank alternatives in equilibrium solutions. By building
the size relations of the potential of interval grey number, Mi and Fang (2005) proposed the
position dominant strategy of grey potential and defined the pure strategy solution. On
this point, Fang and Liu (2006) further introduced a condition of the optimal pure strategy
and solution, as well as discussed the risks that game players face. Fang and Liu (2006)
also researched the symmetrical loss information of game-equilibrium in a group of N
people to define the grey situation-pure-tactical Nash equilibrium to make it easier to find
the equilibrium of the pure grey situation up-and-down approach.

It is necessary to mention the size relations of the grey number while studying grey
games equilibrium. The main methods to compare the size of the interval grey number
include grey position comparison (Fang and Liu, 2003a, b, c; Mi and Fang, 2005),
simple grey number comparison (Fang and Liu, 2003a, b, c) and the probability
distribution of the grey number (Xie and Liu, 2009).

Grey games is mostly based on the traditional game theory but also considers the
profit and loss value of the symmetrical defect by using a strategy analysis method. In
cases using conflict analysis of situation analysis of metagame theory (Howard, 1

6),
the results will be much closer to the result of actual conflict. By simplifying the
algorithms and adding more constraints, Fraser and Hipel (1979) proposed the F-H
conflict analysis method. This method is more complete and compatible with actual
conditions. It is expected to illustrate the essence structure of the objective world and
establish a conflict model by extracting large complex and irregular information based
on players’ strengths, attitudes and goals which are arranged in the order of preferences.
The conflict equilibrium solutions are found by analyzing players’ stability.

Kilgour et al. (1987, 1

3) published the graph model for conflict resolution (GMCR)
based on the idea of the F-H method. In GMCR, solution concepts, which characterize
DM’s possible patterns in conflicts, play an important role to calculate the equilibrium
solution. To depict a diversity of decision types, a variety of solution concepts has been
put forward such as Nash stability (Nash, 1950, 1951), general metarationality (GMR)
(Howard, 1971), symmetric metarationality (SMR) (Howard, 1971), sequential stability
(SEQ) (Fraser and Hipel, 1979), limited-move stability (Fang et al., 1993) and non-myopic
stability (Kilgour, 1984). The GMCR has been applied widely to environment conflict
(Obeidi et al., 2002), business negotiation (Hipel et al., 2001; Xin et al., 2005), engineering
negotiation (Moustafa et al., 2006) and so on. However, this method requires decision
makers (DMs) to provide preference information which is hard to satisfy in real conflicts.

For that reason, this paper discusses the conflict analysis of game theory and
metagame theory in grey system and introduces the grey conflict analysis model based on
the game theory framework by transforming from the static game into the expansion of
the dynamic game. The computation of grey potential, weakening the preferred conflict
analysis and DMs’ state transition, will expand the Nash equilibrium of the original grey

GS
3,

potential pure strategy (adding one more consideration for equilibrium solution). This
renders the game model closer to the reality and allows the intuitive sense of humans to
have greater applicability.

2. Basic concepts of grey game
2.1 Basic definitions of grey game with pure strategy
Definition 2.1. (Grey matrix) For each element of any certain matrix, if there exists grey
number aij(^) (i ¼ 1, 2, . . . , m; j ¼ 1, 2, . . . , n), then this matrix is called grey number
matrix and used A0ð^Þ ¼ ðaijð^ÞÞm£n ði ¼ 1; 2; . . . ; m; j ¼ 1; 2 . . . ; nÞ to represent.

Definition 2.2. (Grey matrix game theory) In the two-person zero-sum finite games,
players set the profit and loss matrix as grey matrix, then we call this matrix grey
matrix game and denote as G0(^) ¼ {S01, S

0
2; A

0(^)}, where S01 ¼ {a
0
1, a

0
2, . . . , a

0
m} is the

set strategies of player 1 and S02 ¼ {b
0
1, b

0
2, . . . , b

0
m} is that of player 2

. A

0(^) is players’
grey profit and loss matrix.

Definition 2.3. (Symmetrical incompleteness of profit and loss value information)
In a game, we use the interval grey number to represent the profit and loss value
information, which is mutual knowledge, thus in this situation the profit and loss value
of the game is named defect and listed as U(^) ¼ {u1(^), u2(^), . . . , un(^)}.

Remark. In order to make it easier to understand, in this paper, all grey numbers
are limited as interval grey numbers as interval grey numbers in various types of grey
numbers are the most representative.

Definition 2.4. (The static game of the profit and loss value information
symmetrical defect) In a game, the profit and loss value information U(^) ¼ {u1(^),
u2(^), . . . , un(^)} and players’ corresponding set of strategies is called S(^) ¼ {s1(^),
s2(^), . . . , sn(^)} then this static game of the profit and loss value symmetrical defects
of the game is set as G(^) ¼ {S(^), U(^)}, simplified as G(^).

For example, in a relatively closed color TV market, there are two oligopoly
manufacturers. In order to seize more market share, they decide whether to decrease- or
not-decrease-price strategy. In the real world, the profit and loss matrix is not clear and
accurate but in terms of grey matrix, therefore we can use the interval grey numbers
[aij, bij] [cij, dij] to represent this. Where [aij, bij] indicates that for manufacturer 1,
because of the income value information of related defect, the corresponding revenue
value is interval grey number; aij represents the minimum income that manufacturer
1 can achieve in this case, bij represents the maximum income that can be achieved
using this strategy. Similarly, cij, dij are those of manufacturer 2 (Table I).

To be able to conduct the equilibrium analysis on the profit and loss value
information symmetrical defect game mentioned above, there must be a method that
can determine the size of the interval grey number. In some cases where the interval
grey number is not easy to distribute clearly, the size comparison of the interval grey
number is a trend. In this paper, we use the grey potential to compare the size of the
interval grey number.

Manufacturer

Decrease Not-decrease

Manufacturer 1 Decrease [a11, b11], [c11, d11] [a12, b12], [c12, d12]
Not-decrease [a21, b21], [c21, d21] [a22, b22], [c22, d22]

Table I.
The grey game between

two manufacturers

Conflict analysis
97

2.2 Compare the size of the interval grey number
Given any two interval grey number ^ij [ [aij, bij] and ^st [ [ast, bst], where
bst $ bij $ ast (Figure 1). Based on the value of the endpoints position of the two grey
numbers, we can split into three intervals, [aij, ast], [ast, bij], [bij, bst], where [ast, bij] is the
intersection area of two grey numbers.

(1) Equipollence potential degree. Consider the intersection area of two grey numbers
in the equilibrium region, set EPDij!st ¼ ðbij 2 astÞ=ðbij 2 aijÞ as grey number ^ij is
the equipollence potential degree of ^st. Similarly, set EPDst!ij ¼ ðbij 2 astÞ=ðbst 2 astÞ
as grey number ^st is the equipollence potential degree of ^ij.

(2) Superiority potential degree. Based on the value of the endpoints position of two
grey numbers, we set [bij, bst], on the right side of the intersection area, as the
superiority region and SPDst!ij ¼ ðbst 2 aijÞ=ðbst 2 astÞ as grey number ^st is the
superiority potential degree of ^ij.

(3) Inferior potential degree. Similarly, we set [aij, ast], on the left side of the
intersection area, as the inferior region and IPDij!st ¼ 2ðast 2 aijÞ=ðbij 2 aijÞ as grey
number ^ij is the inferior potential degree of ^st.

The sum of superiority potential degree and inferior potential degree of any given
interval grey numbers ^ij [ [aij, bij] and ^st [ [ast, bst] is called potential difference,
simply called potential:

. If SPDij!st þ IPDij!st . 0, then we say grey number ^ij is advantageous to grey
number ^st and denoted ^ij s ^st.

. If SPDij!st þ IPDij!st , 0, then we say grey number ^ij is disadvantageous to
grey number ^st and denoted ^ij a ^st.

. If SPDij!st þ IPDij!st ¼ 0, then we say grey number ^ij is equivalent to grey
number ^st and denoted ^ij , ^st.

The set of size relation of grey number potential is a whole set which was detailed by
Fang and Liu (2006). Although the size of grey number potential is not always the real
size of grey number, it is helpful for people’s decision making under the conditions of
defect information, as well as providing new research tools and ideas to search for the
potential equilibrium policy of grey game.

As mentioned above, the size of grey number is expressed in terms of a pair of
binary relations ( s , ,). It is assumed to possess the following properties:

. s is asymmetric, i.e. for any grey number ^ij, ^st, ^ij s ^st and ^ij a ^st
cannot hold true at the same time.

. , is reflexive, i.e. ^ij , ^ij and symmetric, i.e. if ^ij , ^st then ^st , ^ij.

. ( s , ,) is complete, i.e. for any grey number ^ij, ^st, then one of ^ij s ^st,
^ij a ^st or ^ij , ^st is true.

Figure 1.
The relationship of grey
interval numbers

Number
axis

[aij, bij] [ast, bst]

aij bijast bst

GS
3,1

3. The grey conflict analysis model
We use V ¼ {N, S, P, (S, A)} to denote the grey conflict analysis model. N represents
for a non-empty set of players. In this paper, there are two-players, so N ¼ {i, j}, each
player chooses one strategy, so the group of players’ strategies is a situation (a state)
(in order to make it unanimous, in this article, every strategy group is called a state). S,
P stand for the non-empty set of all feasible states and the preference of each DM for
each state, respectively, (according to the merits degree gained from the size
comparison of grey potential). (S, A) indicates the set of all DMs of the state transition.

3.1 Graph model and conflict analysis
There are a few ways to define the equilibrium solutions of grey conflict analysis at first. In
the conflict analysis, using graph theory to represent the conflict, a directed graph is
defined as two-dimension (S, A), where S ¼ {s1, s2, . . . , sn} is vertices set (each point
represents for a situation); A ¼ {a1, a2, . . . , an} has an arc that can change the situation
causing by the change off DMs. The tail of arc means the original situation; the head of arc
denotes the next situation; each DM responds to a graph and reachable matrix (Figure 2).
For that, we can define the reachable matrix Ri(n£n) of DM:

Riðs; qÞ ¼
1; if DM can move from state s to state q in one step

0; others

(

Figure 2.
The analysis procedure

of the grey conflict
analysis model

Conflict

Decision

makers

Options

Feasible states

Profit and loss
value

Grey potential

Preference

Individual
stabilities

Equilibrium

Information to
assist decision

makers

Modeling

Analysis

Conflict analysis
99

From the above reachable matrix, we can get the set of player i’s reachable Ri(s) from
state s:

RiðsÞ ¼ {q [ S : Riðs; qÞ ¼ 1}

A unilateral improvement means that a DM moves from a particular state to a
preferred state. To represent unilateral improvements, each player’s reachability
matrix Ri can be replaced by R

þ
i , defined by:

R
þ
i ðs; qÞ ¼

1; if Riðs; qÞ ¼ 1; and piðsÞ a piðqÞ

0; others
(

Similarly, the set of player i’s unilateral improvements from state s can be defined by:

R
þ
i ðsÞ ¼ {q [ S : R

þ
i ðs; qÞ ¼ 1}

According to the above several ways, the definitions of equilibrium solution under grey
game theory are as follows.

3.2 Equilibrium solutions under grey potential
In the grey conflict analysis model, if a DM has no incentive to deviate from a certain
state then this state is considered stable. If a state is stable for all DMs, it is an
equilibrium state and is regarded as a possible resolution of the conflict.

Definition 3.1. (Grey potential-Nash equilibrium), simplified as GP-Nash.
Let i [ N. A state s [ S is GP-Nash stable for DM i, denoted by s [ S

GP-Nash
i ,

iff (if and only if ) R

þ
i ðsÞ ¼ F.

Additionally, s is said to be an equilibrium state of GP-Nash if s [ S
GP-Nash
i for all

i [ N.
From Definition 3.1 we can get: under GP-Nash equilibrium stability, there is no

unilateral improvement for DM i, when it transferred to other state, the rest states must
become disadvantages to the initial state, the initial state of the choices is the final state.

Definition 3.2. (Grey potential-general metarationality), simplified as GP-GMR.
Let i [ N. A state s [ S is GP-GMR stable for DM i, denoted by s [ S

GP-GMR

i , iff for

every s1 [ R
þ
i ðsÞ, there exists at least one s2 [ Rj (s1), such that pi (s2) # pi (s).

Additionally, s is said to be an equilibrium state of GP-GMR if s [ S
GP-GMR
i for all

i [ N.
In Definition 3.2 “ # ” is equivalent to “ a ” or “ , ”. Player i deems that the

opponent will sanction i’s improvement at any cost.
Definition 3.3. (Grey potential-symmeral metarationality), simplified as GP-SMR.
Let i [ N. A state s [ S is GP-SMR stable for DM i, denoted by s [ S

GP-SMR

i , iff for

every s1 [ R
þ
i ðsÞ, there exists s2 [ Rj (s1), such that pi (s2) # pi (s) and pi (s3) # pi (s) for

all s3 [ Rj (s2).
Additionally, s is said to be an equilibrium state of GP-SMR if s [ S

GP-SMR
i for all

i [ N.
GP-SMR solution is similarly to GP-GMR, however, for player i, there is still an

opportunity to counter-back and the conflict ends after his or her counter-move.
Definition 3.4. (Grey potential-sequential stability), simplified as GP-SEQ.

GS
3,1

100

Let i [ N. A state s [ S is GP-SEQ stable for DM i, denoted by s [ S

GP-SEQ

i , iff for

every s1 [ R
þ
i ðsÞ, there exists at least one s2 [ R

þ
j ðs1Þ, such that pi (s2) # pi (s).

Additionally, s is said to be an equilibrium state of GP-SEQ if s [ S
GP-SEQ
i for all

i [ N.
GP-SEQ solution is similarly to GP-GMR, the only difference is that the opponent

will sanction i’s improvement, but only using their own improvements.
The first column of Table II describes the approaches of different solution concepts

to foresight which measures the maximum number of moves foreseen by a DM

;

GP-Nash stability has foresight one; the other definitions (GP-GMR, GP-SMR and
GP-SEQ) have foresight two or three.

The disimprovement criterion indicates a DM’s willingness to move to a less
preferred state. In GP-Nash and GP-SEQ stability, disimprovements cannot be
accepted and in GP-GMR and GP-SMR, only disimprovements by opponents with the
purpose of sanctioning are allowed.

The last column of Table II shows the knowledge of preferences in the viewpoint of
DM’s. Under GP-Nash, GP-GMR and GP-SMR, opponents’ preference rankings are not
required. But under GP-SEQ stability, preference rankings for the focal DM and his
opponent are required.

3.3 Interrelationships of solution concepts

Theorem 3.1. S

GP-Nash
i

# SGP-SMR
i

;

SGP-Nash
i

# SGP-GMR
i

; SGP-Nash
i

# S

GP-SEQ
i

Proof. For i [ N, if state s [ S
GP-Nash
i , then R

þ
i ðsÞ ¼ F, which implies Definitions

3.2-3.4, are satisfied because no s1 belongs to R
þ
i ðsÞ. Hence s [ S

GP-GMR
i , s [ S

GP-SMR
i ,

s [ S
GP-SEQ
i . This proves that S

GP-Nash
i
# SGP-SMR
i
; SGP-Nash
i
# SGP-GMR
i
;
SGP-Nash
i
# SGP-SEQ
i
. A

Theorem 3.2. SGP-SMR
i

# SGP-GMR
i

.
Proof. For i [ N, if state s [ S

GP-SMR
i , two cases may arise. First, R

þ
i ðsÞ ¼ F. In

this case, s [ S
GP-Nash
i , and hence, s [ S

GP-GMR
i according to the theorem 3.1. Second,

R
þ
i ðsÞ – F. Because s [ S

GP-GMR
i , according to Definition 3.3, for every s1 [ R

þ
i ðsÞ,

there exists s2 [ Rj (s1) such that pi (s2) # pi (s), and pi (s3) # pi (s) for all s3 [ Rj (s2).
Discarding the information about s3, it is easy to see that Definition 3.2 is satisfied.

Hence, s [ S
GP-SMR
i as well. This proves that S

GP-SMR
i # S

GP-GMR
i . A

Theorem 3.3. S GP-SEQ # S GP-GMR.
Proof. For i [ N, if state s [ S

GP-SEQ
i , again, two cases may arise. First, R

þ
i ðsÞ ¼ F.

In this case, s [ S
GP-Nash
i , therefore, s [ S

GP-GMR
i according to the above argument.

Second, R
þ
i ðsÞ – F. Because s [ S

GP-SEQ
i , for every s1 [ R

þ
i ðsÞ, there exists at least one

Foresight Disimprovements Knowledge of preferences

GP-Nash 1 Never Own
GP-GMR 2 By opponents Own
GP-SMR 3 By opponents Own
GP-SEQ 2 Never All

Table II.
The differences between

equilibrium solutions

Conflict analysis

101

s2 [ R
þ
j ðs1Þ such that pi (s2) # pi (s). However, s2 [ R

þ
j ðs1Þ # Rjðs1Þ, so, according to

Definition 3.2, state s [ S
GP-GMR
i . This proves that S

GP-SEQ
i
# SGP-GMR
i

. A
The logical relationships among four stability solutions as follows:

S GP-Nash # S GP-SMR # S GP-GMR; S GP-Nash # S GP-SEQ # S GP-GMRand as shows in Figure 3.

4. Example
In a relatively closed colored TV market, let’s consider the problem of “prisoner’s
dilemma” between two oligopoly manufacturers. Due to several reasons, their profit
and loss value information are symmetry detect, the value (unit: million) can be used by
interval grey number, as shown in Table III.

4.1 DMs, options and states
There are two DMs, as shown in the “prisoner’s dilemma” above. Manufacturers 1 and 2,
we simply denote as DM1, DM2, respectively. DM1 has two options: decrease price or
not-decrease price, so does DM2. Therefore, this game includes four states: s1 (decrease,
decrease), s2 (decrease, not-decrease), s3 (not-decrease, decrease), s4 (not-decrease,
not-decrease).

4.2 Grey potential and preference information
According to the definition of grey potential in part 2, we can calculate the superiority
potential degree and inferior potential degree of four states.

For DM1, We use these following formulas to calculate the superiority potential
degree and the inferior potential degree between state s1 (decrease, decrease) and state

(not-decrease, decrease):

SPDs1!s3 ¼
1 2 0

1 2 ð21Þ
¼

2
IPDs1!s3 ¼ 2

ð22Þ 2 ð21Þ

1 2 ð21Þ
¼
1
2

Then:

SPDs1!s3 þ IPDs1!s3 ¼
1

2
þ

2
¼ 1 . 0

Figure 3.
Interrelationships of
solution concepts

GP-SEQ
GP-SMR
GP-GMR

GP-
Nash

Manufacturer 2
Decrease Not-decrease

Manufacturer 1 Decrease [21, 1], [21, 1] [1, 2.5], [22, 0]
Not-decrease [22, 0], [1, 2.5] [0, 2], [0, 2]

Table III.
The grey profit and loss
matrix between two
manufacturers

GS
3,1

102

So, for manufacturer 1, state s1 is advantageous to state s3; similarly, we can conclude
that state s2 is better than state s4, and state s4 is advantageous to state s1; according to
the property of preference, we can get the preference information of manufacturer 1 as
follows:

P1 : s2 s s4 s s1 s s3

For DM2, the calculation of the superiority potential degree and the inferior potential
degree between state s3 (not-decrease, decrease) and state s4 (not-decrease, not-decrease)
as follows:

SPDs3!s4 ¼
2:5 2 2

2:5 2 1
¼

3
IPDs3!s4 ¼ 2

0 2 1

2:5 2 1
¼
2

3
Then:

SPDs3!s4 þ IPDs3!s4 ¼
1

3
þ

3
¼ 1 . 0

So, for manufacturer 2, state s3 is advantageous to state s4; similarly, we can conclude
that state s1 is better than state s2 and state s4 is advantageous to state s1; according to the
property of preference, we can get the preference information of manufacturer 2 as
follows:

P2 : s3 s s4 s s1 s

4.3 Graph model
When manufacturer 2 chooses the decrease strategy, for manufacturer 1, he can move
from decrease to not-decrease, also, he can move from not-decrease to decrease; he can
transform between state s1 and state s3; manufacturer 1 can transform between state s2
and state s4 when manufacturer 2 selects the not-decrease strategy.

Similarly, we can get the state transition of manufacturer 2. The graph model of
DM1 and DM2 as shown in Figure 4.

4.4 Equilibrium states and analysis
According to Definitions 3.1-3.4, the process to calculate equilibrium is as follows.

Considering state s1 (decrease, decrease): because R
þ
1 ðs1Þ ¼ F, so the state s1 is

GP-Nash equilibrium state for DM1; additionally, because R
þ
2 ðs1Þ ¼ F, so the state s1 is

GP-Nash equilibrium state for DM2. Therefore, state s1 is GP-Nash equilibrium. From
the logical relationships among equilibrium solutions, we can conclude that state s1 is
also GP-GMR, GP-SMR and GP-SEQ equilibrium state.

Let’s consider state 4 for DM1 to explain why a state possessing a unilateral
improvement can be GP-GMR stable. The diagram is shown in the first graph in
Figure 5. DM1 can make a unilateral improvement to state 2 or else stay at state 4.

Figure 4.
Graph model for

DM1 and DM2s3

a1 a2 a3

s1 s2

s3 s4

Conflict analysis

103

From state 2, DM2 can move to state 1 or else stay at state 2. However, notice that state
1 is less preferred than state 4 by DM1, so DM1 is willing to stay at the initial state and
then state 4 is GP-GMR stable for DM1.

Notice that when DM2 moves from state 2 to state 1, state 1 is more preferred than
state 2 for DM2, so the state 4 is also GP-SEQ stable.

The GP-SMR stable as shown in the second graph in Figure 5, is similar to
Figure 4(a), the only difference is that the game is not over when DM2 moves to state 1
and the DM1 has the chance to move from state 1 to state 3. While we notice that state 3
is also less preferred than the initial state 4, so DM1 is willing to stay at state 4 and then
state 4 is GP-SMR stable for DM1.

The unstable state is shown the third graph in Figure 5. DM1 can make a unilateral
improvement move from state 3 to state 1 or else stay at state 3. From state 1, DM2 can
move to state 2 or else stay at state 1. However, notice that state 2 is preferred than
state 3 by DM1, so DM1 is willing to move, then state 3 is not stable for DM1.

Similarly, we can analysis the equilibrium states of DM2; the final equilibrium states
as shown in Table IV.

In Table IV, “1”, “2” indicate DM1 and DM2, respectively; “E” is the abbreviation of
“equilibrium”, “U” denotes that the state is a stable state under the equilibrium
solution. For example, state s2, it is GP-Nash stable state for DM1, but it’s not GP-Nash
stable state for DM2; while, state s1, it’s GP-Nash stable for both DM1 and DM2, then the
state is GP-Nash equilibrium.

From the results of equilibrium states in Table IV, we can conclude as follows: when
considering the GP-Nash equilibrium, only one state s1 (decrease, decrease) is the final
equilibrium state, which is consistent with the classical game theory. All DMs are

Figure 5.
The diagram of calculate
equilibrium solutions

s4
s4
s4
s4
s2
s2
s2
s2

s2s1

Note: “s” means “stay”

s1
s1
s1
s1
s3
s3
s3

DM1

DM2

DM1
DM2
DM1
DM1
DM2
s
s
s
s
s

s
s

GP-Nash GP-GMR GP-SMR GP-SEQ
1 2 E 1 2 E 1 2 E 1 2 E

s1 U U U U U U U U U U U U
s2 U U U U
s3 U U U U
s4 U U U U U U U U U

Table IV.
The final
equilibrium states

GS
3,1

104

considering the best of personal, but in fact, the individual interest has conflict with the
collective interest. That is the “prisoner’s dilemma”. When we consider the GP-GMR,
GP-SMR and GP-SEQ solutions, we can find that except state s1 is the stable state, state s4
(not-decrease, not-decrease) is also the stable state. The main reason is that: the DM
considers only one step under GP-Nash equilibrium. The explanation is that the DM is
short-sighted and has no long-term vision. In contrast, the DM will consider multiple steps
under the GP-GMR, GP-SMR and GP-SEQ stability. Therefore, for a sufficient farsighted
DM, he or she will select state s4 (not-decrease, not-decrease) as the last equilibrium state.

5. Conclusions and future work
In this paper, we combine the grey game theory with the GMCR in two persons based
on pure strategy and construct the grey conflict analysis model. Detailed contributions
along this research include:

. From the number of DM’s steps, pure strategy GP-Nash solution was extended to
GP-GMR, GP-SMR and GP-SEQ concepts.

. Interrelationships of solution concepts were investigated; theoretical results
established interrelationships of the four solution concepts.

. An illustrative example was developed to demonstrate how the grey conflict
analysis model and these solution concepts can be applied, the example results of
this paper showed that the proposed model is reliable and reasonable.

The proposed method in this paper establishes a hybrid framework for conflict
analysis by combining grey game and GMCR together. The hybrid system that
extends GMCR by allowing preference to be expressed in grey interval values is more
general than existing grey game theory and GMCR.

To allow complex cases such as economic and social applications to be efficiently
and expeditiously analyzed, the two-player game will be extended to n-players in the
near future.

References

Deng, J.L. (1982), “The control problems of grey systems”, Systems and Control Letters, Vol. 1
No. 5, pp. 288-94.

Fang, L.P., Hipel, K.W. and Kilgour, D.M. (1993), A Decision Support System for Interactive
Decision Making: The Graph Model for Conflict Resolution, Wiley, New York, NY.

Fang, Z.G. and Liu, S.F. (2003a), “Grey matrix game model based on pure strategy”, Journal of
Nanjing University of Aeronautics and Astronautics, Vol. 35 No. 4, pp. 441-5.

Fang, Z.G. and Liu, S.F. (2003b), “Pure strategy solution and venture problem of grey matrix
game based on undeterminable directly interval grey number”, Journal of Jilin University
(Engineering and Technology Edition), Vol. 36 No. 1, pp. 137-42.

Fang, Z.G. and Liu, S.F. (2003c), “Study on grey matrix game based on pure strategy (I): building
on normal grey matrix game”, Journal of Southeast University (Natural Science Edition),
Vol. 33 No. 6, pp. 796-800.

Fang, Z.G. and Liu, S.F. (2006), “Matrix game of grey situation-pure-tactical Nash equilibrium in
symmetrical loss information of game-equilibrium in n-people”, Proceeding of Modern
Industry Engineering and Management, pp. 70-4.

Fraser, N.M. and Hipel, K.W. (1979), “Solving complex conflicts”, IEEE Transactions on Systems,
Man and Cybernetics, Vol. 9 No. 12, pp. 805-17.

Conflict analysis

105

Hipel, K.W., Kilgour, D.M., Fang, L.P. and Peng, X. (2001), “Strategic decision support for the services
industry”, IEEE Transactions on Engineering Management, Vol. 48 No. 3, pp. 358-69.

Howard, N. (1971), Paradoxes of Rationality: Theory of Metagames and Political Behavior, MIT
Press, Cambridge, MA.

Howard, N. (1976), “Prisoner’s dilemma: the solution by general matagames”, Behavioral Science,
Vol. 21 No. 6, pp. 524-31.

John, V.N. and Osakar, M. (1944), The Theory of Games and Economic Behavior, The Press of
Princeton University, Princeton, NJ.

Kilgour, D.M. (1984), “Equilibria for far-sighted players”, Theory and Decision, Vol. 16, pp. 135-57.

Kilgour, D.M., Hipel, K.W. and Fang, L.P. (1987), “The graph model for conflicts”, Automatica,
Vol. 23 No. 1, pp. 41-55.

Luo, D. and Wu, S.X. (2005), “Research on binotary finite zero-sum in grey games with mixed
strategy”, Journal of Xiamen University (Natural Science), Vol. 44 No. 3, pp. 318-21.

Luo, D. and Wu, S.X. (2006), “Research on two-person zero-sum in finite games with grey uncertain
restriction”, Journal of Xiamen University (Natural Science), Vol. 45 No. 1, pp. 29-32.

Mi, C.M. and Fang, Z.G. (2005), “Study on strategy dominance and pure strategies solution of
grey matrix game based on interval grey number not to be determined directly”, Chinese
Journal of Management Science, Vol. 13 No. 6, pp. 81-5.

Moustafa, K., Keith, H. and Tarek, H. (2006), “Conflict resolution in construction disputes using
the graph model”, Journal of Construction Engineering and Management, Vol. 132 No. 10,
pp. 1043-52.

Nash, J.F. (1950), “Equilibrium points in n-person games”, Proceedings of National Academy of
Science, Vol. 36, pp. 48-9.

Nash, J.F. (1951), “Non-cooperative games”, Annals of Mathematics, Vol. 54 No. 2, pp. 286-95.

Obeidi, A., Hipel, K.W. and Kilgour, D.M. (2002), “Canadian bulk water exports: analyzing the
sun belt conflict using the graph model for conflict resolution”, Knowledge, Technology
and Policy, Vol. 14 No. 4, pp. 145-63.

Tao, Y., Liu, S.F. and Fang, Z.G. (2004), “Solution of grey matrix game based on grey mixed strategy”,
Journal of Nanjing University of Aeronautics & Astronautics, Vol. 36 No. 4, pp. 524-7.

Xie, N.M. and Liu, S.F. (2009), “On comparing grey numbers with their probability distributions”,
Systems Engineering-Theory & Practice, Vol. 29 No. 4, pp. 169-75.

Xin, S., Ye, C., Keith, W.H. and Kilgour, D.M. (2005), “Comparison of the analytic network process
and the graph model for conflict resolution”, Journal of Systems Science and Systems
Engineering, Vol. 14 No. 3, pp. 308-25.

Further reading

Howard, N. (1987), “The present and future of metagame analysis”, European Journal of
Operational Research, Vol. 32 No. 1, pp. 1-25.

Liu, S.F., Dang, Y.G. and Fang, Z.G. (2004), Grey Systems Theory and Its Applications, The Science
Press of China, Beijing.

Corresponding author
Haiyan Xu can be contacted at: xuhaiyan@nuaa.edu.cn

To purchase reprints of this article please e-mail: reprints@emeraldinsight.com
Or visit our web site for further details: www.emeraldinsight.com/reprints

GS
3,1
106

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

AmericanJournal Of Business Education – July/August 2013 Volume 6, Number 4

2013 The Clute Institute Copyright by author(s) Creative Commons License CC-BY 459

Comparing Correlations Between

Four-Quadrant And Five-Factor

Personality Assessments
Cathleen S. Jones, Robert Morris University, USA

Nell T. Hartley, Robert Morris University, USA

ABSTRACT

For decades, some of the most popular devices used in educating students and employees to the

values of diversity are those that are based on a four-grid identification of behavior style. The

results from the scoring of the instruments provide individual profiles in terms of a person’s

assertiveness, responsiveness, and preferred tone of interacting with his environment. In the past

decade, a five-factor framework has gained in popularity as an assessment instrument. The scope

of the current paper is a comparison of a four-factor instrument (questionnaire) to a five-factor

instrument (questionnaire) to establish correlations between the two. If the information can be

seen as being complimentary rather than disconnected, then users will benefit from synergy as

they encounter different instruments throughout their careers. Also, duplication of effort in terms

of using multiple instruments may be reduced.

Keywords: Personality Assessment; DISC; Five-Factor Model; Education; Organizational Behavior

INTRODUCTIO

eople have always tried, through anecdotal evidence, to make assumptions and develop myths and

superstitions that impact their lives (example: money can buy happiness . . . as long as you spend it

on other people). The importance of individuality in understanding behavior is best expressed by

Kurt Lewin, a neo-gestalt, in his formula: B=f(e x p). The behavior of any one person is due to who he is and the

environment in which he finds himself. While it is human nature to observe and pass judgment (categorize) the

people with whom we interact, based on anecdotal evidence, science offers a more reliable way of assessing others

and ourselves. Lewin was at the forefront of scholars who believed that a basic purpose of any science is to develop

theory. Theories are carefully worded statements specifying relations among variables that explain and predict what

will happen. In this paper, we seek to relate theory to practice. The purpose of one is to generate knowledge; the

purpose of the other is to be able to put the knowledge into practice (Sanderlands n.d.). Our understanding of the

transfer of knowledge encourages us to explore ways in which commonalities of theories lead to comprehension and

practice of knowledge.

In this paper, the micro unit of behavioral study is that of individual personality. Personality instruments

provide individual profiles in terms of a person’s assertiveness, approach to decision-making, responsiveness, and

preferred style of interacting with his environment. The two instruments being compared are the four-quadrant

Jungian-based DiSC and the Five-factor Model of Personality.

PURPOSE

Around 80 percent of the Fortune 500 companies use personality tests, such as the Myers-Briggs Type

Indicator, to assess their employees for the purpose of coaching, development, and team building (Dattner, 2008). A

review of the literature supports the need for understanding and validating this popular practice.

http://www.cluteinstitute.com/

http://creativecommons.org/licenses/by/3.0/

http://www.psychologytoday.com/basics/personality

http://www.cpp.com/products/mbti/index.asp

http://www.psychologytoday.com/basics/coaching

http://www.psychologytoday.com/basics/teamwork

American Journal Of Business Education – July/August 2013 Volume 6, Number 4

460 Copyright by author(s) Creative Commons License CC-BY 2013 The Clute Institute

The underlying assumed value of using personal assessments in class is that an understanding of the

knowledge provided will enable the person to become closer to reaching his full potential. Jung predicted

“…modern man can only know himself insofar as he can become conscious of himself” (Jung, 1957, 79). Having

an objective – if not always a 100% accurate descriptive theory of one’s self and the impact that one has on others –

may influence our interpersonal skill acquisition. Personality research supports the theory that recognition of one’s

preferred behavior and preferred environment influences the challenges one accepts and the decisions one is most

likely to make. “There is nothing so practical as a good theory” (Lewin, 1951, 100). The caveat here is that the

knowledge in no way determines what we are able to do.

An increased synergy is anticipated through the generalizations that apply to the results of this study.

Perspectives on learning, leadership, conflict resolution, and communication are natural extensions of personality

awareness. The instruments are based on theories. The reader is reminded that the point of this paper is not to

question the theories, but rather to show the similarities in them and their root derivation. Scholars have shown that

positive transfer occurs when learning in one context improves performance in another context (Perkins, 1992, 3);

i.e., a student who learns in one class that his style tends toward that of a “High I, High S” can build on that

information in a subsequent corporate training session where the trainer prefers to use the Five-factor vocabulary of

“Extravert, Agreeable.” Furthermore, the knowledge of “type/style” will help him further in understanding and/or

communicating with a difficult co-worker who defiantly says, “You just don’t understand me; I’m an ISTJ.”

The

work by Allesandre – the discussion of a “Platinum Rule” – is an additional logical extension of the use of the

theories.

LITERATURE REVIEW

Writings which span popular and scholarly work exhort the importance of self-knowledge. Three such

scholars are Peter Senge, Daniel Goleman, and Peter Drucker. Peter Senge, in his well-received materials on

“learning organizations”, writes on the importance of the personal mastery which is defined as “learning to expand

our personal capacity to create the results we most desire, and creating an organizational environment which

encourages all its members” (Senge, Kleiner, Roberts, Ross, & Smith, 1994, pg. 6). It is his belief that people with a

high level of personal mastery achieve results that matter most to them personally. “People who excel in these skills

(personal awareness) do well at anything that relies on interacting smoothly with others; they are social stars”

(Goleman, 1995, 43-44). “And yet, a person can perform only from strength. One cannot build performance on

weaknesses, let alone on something one cannot do (or be) at all.” (Drucker 2005, 100)

Conventional wisdom is that each of us is unique because no environmental experiences of the genetic pool

are the same for any two people. Our personalities are an important determinant of our behavior. “Because

personality is an important determinant of how a person thinks, feels, and behaves, it is helpful to distinguish

between different types of personalities.” (Staw, 2004, p. 7) This idiographic research seeks to correlate data from

two differently constructed assessment tools – the four-quadrant DiSC and the Five-factor Personality Assessment.

As early as 400 BC, Hippocrates was trying to categorize personality types in an effort to understand individual

differences. It was a more recent scholar – Carl Jung – who discovered that one’s psychological make-up,

“temperament”, “style”, or “type” influences and limits one’s judgment and establishes one’s relationship to the

world. Over 1,400 dissertations, theses, books, and journal and newspaper articles have been published on these

personal inventories. The fundamental assumption behind identifying core responses and needs is that what may

seem like a random variation in behavior (i.e., clean car vs. dirty car people) occurs not by accident but by

observable differences in mental functioning – the way in which people prefer to gather, process, and disseminate

information.

Despite the variety of names used in the four-quadrant instruments to connote a person’s place in the grids

(Otter, INTF, Compliant, Color Yellow) and the proliferation of instruments, there is no appreciable difference in

concept and/or information (Motley & Hartley, 2005). There is alignment in information provided. The four-

quadrant instrument used in this research is the DiSC which takes its name from four basic types of behavior –

dominance, influencing, steadiness, and compliance. The current version is based on the works of Swiss

Psychologist Carl Jung and, later, by Americans William Marston, Walter Clark, Jack Mohler, and Tom Ritt (Ritt,

1980). The Personal DiSC Concept derives its underpinnings from William Marston, a physiological psychologist

http://creativecommons.org/licenses/by/3.0/

http://www.cluteinstitute.com/

American Journal Of Business Education – July/August 2013 Volume 6, Number 4

2013 The Clute Institute Copyright by author(s) Creative Commons License CC-BY 461

writing in the 1920s and 1930s. The DiSC instrument measures surface traits and is intended to explain how they

lead to behavioral differences among individuals (Inscape Publishing, 1996).

In building on Jung’s theory of personality, Marston was concerned primarily with improving human

relationships. “Dr. Marston intended to explain how normal human emotions lead to behavioral differences among

people as well as to changes in a person’s behavior from time to time. His work focused on finding practical

explanations that would help people understand and manage their experiences in the world.” (Inscape Publishing,

1996, Pg. 2) “Marston sought to explain how people adjust to tensions within the environment by looking at their

emotional response to it and then relating this response to behavior.

Described on the discinsights.com website as the most universally accepted test for determining human

behavior, the four quadrants for the DISC personality test are:

 Drive/Dominance (D) – task-oriented, fast-mover, bottom-line-oriented

 Influence (I) – people-oriented, energetic, desire popularity and praise

 Steadiness (S) – very people and family-oriented, motivated by loyalty and security, slower-moving

 Compliance/Conscientiousness (C) – task and detail-oriented, wants all information, slower-moving

The DISC personality test has been taken by more than 50 million people and published in books that

appear in 35 languages (Harlow, T., 2009, October 9). “Studies have revealed that more than 81% of a participant’s

colleagues see DISC Assessment as a very accurate picture of a person’s habitual behavior patterns. Among those

who are primarily “D” in their style, accuracy is rated at 91%; for “I” types, it is 94%. Primarily, “S” type

individuals perceive 85% accuracy, while for “C” types, it is 82%. This gives us an 88.49% perceived accuracy,

with a standard deviation of 6.43%. In other words, the DISC Profile generated by this process is perceived as

highly accurate, in most situations, by most participants” (Personality Insights).

The Five-factor Theory, also known as the Five-factor Model (FFM) or the OCEAN, is based on research

into the concept of grouping of personality descriptors that began as early as 1917 (Goldberg, 1992). Years of

scrutinizing and testing the evolving theory provided a platform for the current model based primarily on the work

of Costa and McCrae. Their work in 1992 benefitted from the work of many independent researchers who had

begun to study known personality traits in order to find the underlying factors of personality (Digman, 1990). The

five factors are in a hierarchy and on a continuum. The theory addresses the relative presence of the following five

traits:

• Openness – open-minded, an interest in art, emotional, adventurous, new ideas, and curiosity
• Conscientiousness – typically self-disciplined, results-oriented and structured, traditional, and dutiful
• Extraversion – high energy level, people person, extrovert, and gets stimulated by being around others
• Agreeableness – compassionate, cooperative, ability to forgive and being pragmatic; let’s get the thing

done

• Neuroticism – sensible, vulnerable, in extreme – emotionally unstable and neurotic

Tables 1 and 2 contain a summary of a literature review presenting the advantages of the DISC personality

assessment and the Five-factor Model.

http://www.cluteinstitute.com/

http://creativecommons.org/licenses/by/3.0/

American Journal Of Business Education – July/August 2013 Volume 6, Number 4

462 Copyright by author(s) Creative Commons License CC-BY 2013 The Clute Institute

Table 1: Advantages of DISC Personality Assessment

Advantages Citation(s)

Frequently used by business organizations Reynierse, J. H., Ackerman, D., Fink, A. A., & Harker, J. B.

(2000). The effects of personality and management role on

perceived values in business settings. International Journal of

Value – Based Management, 13(1), 1-13.

Easy to administer and interpret -Slowikowski, M. (2005). Using the DISC behavioral

instrument to guide leadership and communication. AORN

Journal, 82(5), 835. doi:10.1016/S0001-2092(06)60276-7

-The benefits of using Disc (2010). Retrieved from

http://www.discprofile.com/what-is-disc/benefits.htm

-Spies, R. A., & Plake, B. S. (Eds.). (2005). The sixteenth

mental measurements yearbook. Lincoln, NE: Buros Institute

of Mental Measurements

Has been shown to be a predictor of success in areas such as

employee retention, job success, sales management, and

persuading patients to accept treatment plans that are essential

for their health and well-being

Deviney, D., Mills, L. H., & Gerlich, R. (2010). Environmental

impacts on GPA for accelerated schools: A values and

behavioral approach. Journal Of Instructional Pedagogies, 31-

15.

Proven to be reliable and consistent (2005). Disc validation research report. Inscape Publishing, 1-

22. Retrieved from http://www.discprofile.com/cart/includes/

templates/ppsi/pdfs/1.0/ResearchDiSC_ValidationResearchRe

port

Provides three perspectives: personal, private, and public

which presents a more rounded view of personality

Motley, 2005

Table 2: Advantages of Five-factor Model

Advantages Citation(s)

Able to better understand people who score in the middle range

(in comparison to MBTI (Myer Briggs Type Indicator))

Furnham, A. (1996). The big five versus the big four: The

relationship between the myers-briggs type indicator (mbti)

and neo-pi five-factor model of personality. Pergamon, 21(2),

303-307.

The FFM has been the most widely accepted working

hypothesis of personality structure (1997)

(McCrae & Costa, 1997)

Evidence exists for the criterion-related validity of scores on

FFM measures

Ehrhart, K. H., Roesch, S. C., Ehrhart, M. G., & Kilian, B.

(2008). A test of the factor structure equivalence of the 50-

item ipip five-factor model measure across gender and ethnic

groups. Journal of Personality Assessment, 90(5), 507-516.

Equivalent translations exist in half a dozen languages which

permits wider cross-cultural universality

Thalmayer, A., Saucier, G., & Eigenhuis, A. (2011).

Comparative validity of Brief to Medium-Length Big Five

and Big Six Personality Questionnaires. Psychological

Assessment, 23(4), 995-1009. doi:10.1037/a0024165

Faculty Survey

To confirm the use of personality tests as assessment instruments in courses, a short survey of university

faculty was conducted. An email with a link to the survey was sent and 67 completed responses were received

during the data collection period of September 8-13, 2011.

The sample consisted of 38 women (57.6%) and 28 men (42.4%). Of the sample, 93.8% (61respondents)

listed their highest degree completed as a doctoral. The highest level degree was in Business (68.2%, 45

respondents) and the remaining 31.8% was evenly split between Education, Psychology, and Other. Responses to

the question about years teaching at the college/university level were fairly evenly split among the categories as

shown in Table 3. The survey respondents make up a good representation of university faculty, primarily in the

Business area.

http://creativecommons.org/licenses/by/3.0/

http://www.cluteinstitute.com/

http://www.discprofile.com/what-is-disc/benefits.htm

http://www.discprofile.com/cart/includes/

American Journal Of Business Education – July/August 2013 Volume 6, Number 4

2013 The Clute Institute Copyright by author(s) Creative Commons License CC-BY 463

Table 3: Years Teaching
Frequency Percent

Valid

0-9 18 26.9

10-19 18 26.9

20-29 13 19.4

30+ 17 25.4

Total 66 98.5

Missing System 1 1.5

Total 67 100.0

Fifty-six respondents (83.6%) indicated that they administered personality tests in their courses. Those

who did not stated a variety of reasons, ranging from a lack of understanding of the test instruments to doubt about

the validity to concern about the impact on the students or the course, to an objection to the cost which would not be

reimbursed.

As shown in Table 4, Organizational Behavior was the most frequent response for the question about

courses in which the personality tests were administered, which is not surprising since the prospective respondents

were recruited from an Organizational Behavior-related email list.

Table 4: Course in Which Tests were Administered

# %

Organizational Behavior 44 65.7%

Principles of Management 12 17.9%

Freshman Experience 5 7.5%

Other 16 23.9%

A variety of personality tests was administered by the faculty responding to the survey. As seen in Table 5,

of the two personality instruments discussed in this article, the Big 5 was used much more widely than the DISC

personality test. Results were much more evenly split in terms of how many textbooks included personality tests.

According to the respondents, 59.1% (39) of their textbooks included personality tests.

Table 5: Type of Personality Test/Social Inventory Administered

# %

Myers-Briggs 35 52.2%

Big 5 27 40.3%

DISC 4 6%

Other 20 29.9%

Examining the results of the question of which personality tests are included in textbooks (Figure 1) helps

to explain the results for which personality tests are administered in courses. Of the textbooks that included

personality tests, the majority were Myers-Briggs and/or Big 5. From this brief survey, evidence exists that

personality tests are used in numerous courses.

http://www.cluteinstitute.com/

http://creativecommons.org/licenses/by/3.0/

American Journal Of Business Education – July/August 2013 Volume 6, Number 4

464 Copyright by author(s) Creative Commons License CC-BY 2013 The Clute Institute

Figure 1: Name of Personality Tests/Social Inventories Included in Textbooks

Although the DISC personality assessment received a low number of responses for personality instruments

used in class and personality tests included in the textbook, it is used extensively in industry. Apparently, university

faculties are administering the Big 5 more often in class, but the DISC personality assessment is being used more by

industry. The question then presents itself as to whether knowledge of the Big 5 (Five-factory Theory Model) has

any transferability if students are presented with the DISC personality test at their jobs. The focus of the remaining

analysis will address this question and seek to determine if there is enough of a correlation between these two

personality instruments that knowledge of one instrument will inform people about the other personality test.

METHODOLOGY

Research Design

During a semester-long undergraduate course in Organizational Behavior at a small Northeastern

university, students completed multiple personal assessments. Two of the assessment instruments used were the

“Personal Concept” – also known as DISC by Jack Mohler – and the Five-factor Theory taken from a standard

textbook in Organizational Behavior. Students used unidentifiable code names and recorded the scores for both

instruments. Scores were plotted anonymously. Gender and major were self-reported.

Subjects

People involved in filling out the instruments were participants in an undergraduate class in which the use

of instruments is a central part of the learning experience. All students in the class filled out both personality

instruments. Eighty-nine out of the 110 students reported the results of both personality instruments (approximately

81% of the class). Recording the scores of the instruments is voluntary.

Sample Description

As shown in Table 6, the sample is weighted more heavily toward men than women – almost a 60/40 split;

however, the composition of the class was more male than female. Thus, the sample is a good representation of the

class and both genders were adequately represented. The majority of respondents were management and marketing

students, making up 61.8% of the sample. The breakdown of the majors in the student sample is shown in Table 7.

http://creativecommons.org/licenses/by/3.0/

http://www.cluteinstitute.com/

American Journal Of Business Education – July/August 2013 Volume 6, Number 4

2013 The Clute Institute Copyright by author(s) Creative Commons License CC-BY 465

Table 6: Gender of Respondents
Frequency Percent

Male 55 61.8

Female 32 36.0

Missing 2 2.2

Total 89 100.0

Table 7: Student Major

Number of Respondents Percent of Sample

Accounting 14 15.7

Finance 5 5.6

Hospitality and Tourism Management 3 3.4

Management 34 38.2

Marketing 21 23.6

Sports Management 6 6.7

Other (non-business) 4 4.4

Missing 2 2.2

Total 89 100.0

HYPOTHESES

Overall Hypothesis

There is a strong similarity in the characteristics represented in the four quads theories as represented by

DISC and in the Five-factor theory.

Hypothesis Formation

Hypotheses were formed by comparing the adjectives used to assess each respondent’s personality style,

(Hunter Wells International, 2005; Andre, R., 2008). Synonyms were compared and grouped together as shown in

Tables 8 and 9.

Table 8: DISC Adjectives

D I S C

forceful expressive restrained compliant

Strong-minded emotional satisfied careful

pioneering influential Easy mark correct

domineering attractive willing precise

determined stimulating Even-tempered fussy

demanding captivating patient timid

Self-reliant companionable kind Open-minded

persistent playful Self-controlled agreeable

High-spirited talkative Good-natured Soft-spoken

impatient convincing contented resigned

aggressive Good mixer gentle respectful

nervy poised accommodating conventional

argumentative confident relaxed cooperative

restless inspiring considerate Well-disciplined

courageous optimistic sympathetic diplomatic

positive eager lenient exacting

adventurous enthusiastic loyal adaptable

Will power entertaining Good listener humble

competitive Life-of-the-party obedient tolerant

vigorous persuasive neighborly cautious

outspoken eloquent reserved strict

dogged animated obliging devout

assertive gregarious nonchalant docile

bold outgoing moderate perfectionist

http://www.cluteinstitute.com/

http://creativecommons.org/licenses/by/3.0/

American Journal Of Business Education – July/August 2013 Volume 6, Number 4

466 Copyright by author(s) Creative Commons License CC-BY 2013 The Clute Institute

Table 9: Five-factor Model Adjectives
Introversion/Passivity Extraversion/Energy Conscientious Undirected

Retiring Sociable Well organized Disorganized

Sober Fun-loving Careful Careless

Reserved Affectionate Reliable Undependable

Aloof Friendly Punctual Late

Inhibited Spontaneous Self-reliant Dependent

Quiet Talkative Businesslike Playful

Passive Active Persevering Quitting

Loner Joiner Hardworking Lazy

Task-oriented Person-oriented Practical Impractical

Follower Leader Conscientious Negligent

Traditional (closed) Adventurous (open) Stable Emotional

Conventional Original Calm Worrying

Down-to-earth Imaginative Relaxed High-strung

Uncreative Creative Even-tempered Temperamental

Narrow interests Broad interests Secure Insecure

Not curious Curious Patient Impatient

Unadventurous Daring Not envious Envious, jealous

Conforming Independent Adaptable Vulnerable

Prefer routine Prefer variety Objective Subjective

Traditional Untraditional Comfortable Self-conscious

Inartistic Artistic Self-satisfied Self-pitying

Tough-minded Agreeable

Critical Lenient

Serious Cheerful

Competitive Cooperative

Skeptical Trusting

Argumentative Agreeable

Stubborn Flexible

Egocentric Selfless

Cynical Gullible

Manipulative Straightforward

Proud Humble

Adjectives were compared to each other. Some of the adjectives were exact matches and some were found

using http://thesaurus.yourdictionary.com to find synonyms. Remaining synonyms not found on the website, but

determined to be logical matches, were also included. Symbols for the Hypothesis tables are:

 Synonyms were checked with http://thesaurus.yourdictionary.com.

 *synonyms found in http://thesaurus.yourdictionary.com

 +not found on synonym website, but considered to be a logical match

From the comparison of adjectives for both personality assessment instruments, the hypotheses shown in

Table 10 emerged.

http://creativecommons.org/licenses/by/3.0/

http://www.cluteinstitute.com/

http://thesaurus.yourdictionary.com/

American Journal Of Business Education – July/August 2013 Volume 6, Number 4

2013 The Clute Institute Copyright by author(s) Creative Commons License CC-BY 467

Table 10: Hypothesis Formation

Five-Factor Adjectives DISC Adjectives Hypotheses

Adventurous D Hypothesis #1: The ranking of D is

positively correlated with the ranking of

Adventurous.
Adventurous Adventurous

Original Pioneering

Daring Courageous*, Adventurous+, Bold*

Independent Self-reliant

Tough-minded D Hypothesis #2: The ranking of D is

positively correlated with the ranking of

Tough-minded.
Tough-minded Willpower+

Competitive Aggressive+

Argumentative Competitive+

Stubborn Forceful

Egocentric Argumentative

Proud Determined

Extraversion I Hypothesis #3: The ranking of I is

positively correlated with the ranking of

Extraversion.
Extraversion Outgoing

Sociable Companionable, Good mixer+, Gregarious,

Neighborly*

Fun-loving Entertaining+, Life-of-the-party+

Friendly Outgoing*

Talkative Talkative

Leader Influential+

Persuasive+

Agreeable S Hypothesis #4: The ranking of S is

positively correlated with the ranking of

Agreeable.
Lenient Lenient

Cooperative Accommodating*, Obliging+

Agreeable Kind, Good-natured, Considerate+

Gullible Easy mark+

Stable S Hypothesis #5: The ranking of S is

positively correlated with the ranking of

Stable.
Even-tempered Even-tempered

Patient Patient, Gentle

Not envious Contented+

Comfortable Relaxed

Self-satisfied Contented+

Introversion/Passivity C Hypothesis #6: The ranking of C is

positively correlated with the ranking of

Introversion.
Retiring Timid*

Quiet Soft-spoken+

Follower Compliant+

Conscientious C Hypothesis #7: The ranking of C is

positively correlated with the ranking of

Conscientious.
Careful Careful

Cautious*

Conscientious Precise+, Fussy+

Stable C Hypothesis #8: The ranking of C is

positively correlated with the ranking of

Stable.
Calm Resigned*

Even-tempered Docile+

Adaptable Adaptable

ANALYSIS AND RESULTS

Data consisted of the actual scores for the Five-factor Model and a ranking of the DISC factors. Because

one of the variables (DISC) was ordinal in nature, a Spearman rank correlation coefficient was calculated to test the

hypotheses (Tables 11 and 12). For the correlations, only the left factors were included for the Five-factor Model

(FFM). The FFM left factors are the opposite of the right factors, so it was not considered necessary to test both

sides.

http://www.cluteinstitute.com/

http://creativecommons.org/licenses/by/3.0/

American Journal Of Business Education – July/August 2013 Volume 6, Number 4

468 Copyright by author(s) Creative Commons License CC-BY 2013 The Clute Institute

Table 11: Correlation Matrix (Big Five With DISC)
Ranking for

D I S C

Big 5

Factor One LEFT

Introversion/Passivity

Correlation coefficient

Sig. (2-tailed)

.023

.846

-.383**

.001

.063

.583

.300**

.008

76
Big 5

Factor Two LEFT

Traditional (closed)

Correlation coefficient
Sig. (2-tailed)
N

-.126

.275

-.251*

.029

.234*

.040

.175

.131

76
Big 5

Factor Three LEFT

Tough-minded

Correlation coefficient
Sig. (2-tailed)
N

.278*

.014

-.114

.327

-.308**

.006

.157

.175
76
Big 5

Factor Four LEFT

Conscientious

Correlation coefficient
Sig. (2-tailed)
N

-.039

.737

-.196

.090

.054

.639

.185

.110

76
Big 5

Factor Five LEFT

Stable

Correlation coefficient
Sig. (2-tailed)
N

-.297**

.009

-.032

.781

.275*

.016

77
.008

.946

Total N 86 85 86 85

*Correlations are significant at the .05 level (2-tailed)

**Correlations are significant at the .01 level (2-tailed)

Note: The results were also examined using Kendall’s Tau-b and yielded the same results, so only the Spearman rank correlation

coefficient results are presented here.

Table 12: Results Of Hypothesis Testing: Spearman Rank Correlation Coefficient

Hypothesis #1: The ranking of D is positively

correlated with the ranking of Adventurous.

Not supported: No significant correlation was found.

Hypothesis #2: The ranking of D is positively

correlated with the ranking of Tough-minded.

Supported: A significant positive correlation existed between the

ranking of Tough-minded and D was .278* which was significant at

the .05 level.

Hypothesis #3: The ranking of I is positively correlated

with the ranking of Extraversion.

Supported: I was negatively correlated with Introversion (the opposite

of Extraversion) at the .01 level. The correlation was -.383**.

Hypothesis #4: The ranking of S is positively correlated

with the ranking of Agreeable.

Supported: S was significantly negatively correlated with Tough-

minded at the level of .01 (correlation = -.308). This hypothesis was

supported since Tough-minded is the opposite of Agreeable.

Hypothesis #5: The ranking of S is positively correlated

with the ranking of Stable.

Supported: S was positively correlated with the ranking of Stable

(correlation = .275*; significant at the .05 level).

Hypothesis #6: The ranking of C is positively

correlated with the ranking of Introversion.

Supported: The correlation = .300**; significant at the .01 level.

Hypothesis #7: The ranking of C is positively

correlated with the ranking of Conscientious.

Not supported: no significant correlation found

Hypothesis #8: The ranking of C is positively

correlated with the ranking of Stable.

Not supported: No significant correlation was found.

ADDITIONAL FINDINGS

 D was significantly negatively correlated at the .01 level with the ranking of Stable (correlation = -.297**).

 I was significantly negatively correlated at the .05 level with the ranking of Traditional (correlation = –
.251*).

 S was significantly positively correlated at the .05 level with the ranking of Traditional (correlation =
.234*).

CONCLUSIONS

Eight significant correlations between the Five-factor Model and the DISC personality assessment were

uncovered. Each correlation was consistent with both theories, including the additional correlations which were

found to be significant. No significant correlations contradicted any of the hypotheses. Therefore, a significant

http://creativecommons.org/licenses/by/3.0/

http://www.cluteinstitute.com/

American Journal Of Business Education – July/August 2013 Volume 6, Number 4

2013 The Clute Institute Copyright by author(s) Creative Commons License CC-BY 469

correlation exists between the Five-factor Model and the DISC personality assessment. The logical conclusion is

that knowledge of one of these personality assessments does provide information about the other. An understanding

of the Five-factor Theory Model used more widely in the classroom (according to the survey of university

professors) is likely to help the student understand the DISC personality assessment used more widely in industry.

Knowledge transferability appears to exist at least at some level for these two instruments. Josh Bersin, president

and CEO of Bersin & Associates, an Oakland, Calif., research firm stated, “Personality tests are ‘growing like

wildfire … the employment assessment market overall is worth about $2 billion, up 15 percent from last year.”

(Tahmincioglu, 2011) Also, as seen in the survey of university faculty, the majority of teachers (83.6%) use

personality assessments as part of their course content. Considering the wide use of personality tests at universities

and in the business world, the results of this analysis provide practical application for students seeking to apply what

they have learned at university to the working world. This study has provided recognition that multiple instruments

provide feedback that is complimentary. It is anticipated that with this new knowledge and synergistic application,

the Extravert/lion may actually lie down with the Intravert/lamb.”

FUTURE RESEARCH

Because the study only examined two personality assessments, a natural subject for further study would be

to analyze correlations between additional personality assessment instruments. Of particular interest would be if the

Five-factor Theory and the DISC personality assessment instrument were correlated with the Myers Briggs test

which was used the most by sample respondents (52.2%). Another direction for further research is to document the

connection between the personality descriptors and those describing conflict, learning, leadership, and

communication.

AUTHOR INFORMATION

Cathleen S. Jones is an Associate Professor of Marketing at Robert Morris University specializing in Marketing

Research, Social Media for Marketing, and International Marketing. She holds a Doctor of Science in Information

Systems and Communication from Robert Morris University, an MBA from the Tepper School at Carnegie Mellon

University, and a BA from Westminster College. Her doctoral field project examined the role of health information

and health icons on restaurant menus on restaurant patrons’ food choices. Other areas of interest include working

with Engineering on collaborative interdisciplinary projects and consulting with small businesses and the FDA. E-

mail: jones@rmu.edu (Corresponding author)

Nell Tabor Hartley is University Professor of Management at Robert Morris University. She has taught in the

Graduate School of Education and recently taught in Europe. She holds a B.A. from Agnes Scott College; M.S. from

University of Illinois, and Ph.D. from Vanderbilt University. A focus of her teaching and corporate consulting is

recognition and utilization of individual differences. She has twice received the president’s top teaching award. She

is an elected board member of Organizational Behavior Teaching Society and on the editorial board of Journal of

Management History. E-mail: hartley@rmu.edu

REFERENCES

1. Andre, R. (2008). Organizational Behavior. Upper Saddle River, New Jersey: Pearson Eduction, Inc.
2. Andre, R. (2011). Enhancing the practical application of Five-Factor personality theory. In Int. J.

Management Practice Vol. 4 (pp. 360-375).

3. Barrick, M. R., Mount, M. K., & Salgado, J. (1997). The Five-factor Model of Personality and Job
Performance in the Eurpoean Community. Journal of Applied Psychology, 82.

4. Donner, B. (2008) “Why many companies use some personality assessments and not others” Retrieved
from www.psychologytoday.com/…/the-use-and-misuse-personality-tests-

5. Drucker, P. F. (2002). Managing Oneself in Harvard Business Review on Managing Your Carrer. Harvard
Business School (Reprint 99204).

6. Drucker, P. F. (2005). Managing Oneself. Harvard Business Review, 100-109.

http://www.cluteinstitute.com/

http://creativecommons.org/licenses/by/3.0/

mailto:jones@rmu.edu

mailto:hartley@rmu.edu

http://www.psychologytoday.com/…/the-use-and-misuse-personality-tests-

American Journal Of Business Education – July/August 2013 Volume 6, Number 4

470 Copyright by author(s) Creative Commons License CC-BY 2013 The Clute Institute

7. Fasihizadeh, N., Oreyzi, H., & Nouri, A. (2012). The Relationship between Dominance, Influence,
Steadiness and Conscientiousness (DISC personality profiler) with Myers-Briggs Type Indicator (MBIT)

among the Personnel of One Industrial Company. EuroJournals Publishing, Inc, 95-104.

8. Formerly, C. (1996). SiSC Classic and Models of Personality. Inscape Publishing.
9. George, J. (1992). The Role of Personality in Organizational Life; Issues and Evidence. Journal of

Management, 18(2): 185-213.

10. Goleman, D. (1994). Emotional Intelligence: Why it can matter more than IQ. New York, New York:
Bantam Books.

11. (1995). Emotional Intelligence. In D. Goleman. New York, New York: Bantam Books.
12. Golberg, L. R, (1992) The Development of Markers for the Big Five-factor Structure. Psychological

Assessment, (4): 26-42

13. Hergenhahn, B., & Olson, M. (2007). An Introduction to Theories of Personality . Prentice Hall: Pearson
Education.

14. Hunter Wells International, 1976, revised 2005. 115 5
th

Green Court Atlanta, GA. 30350.

15. Jung, C. (1953). Two essays on analystical psychology. In A. M. Forham, H. Read, & C. Jung. New York:
Pantheon Books.

16. Jung, C. (1957). The Undiscovered Self. New York, New York: First Signet Printing.
17. Jung, C. (n.d.). The Undiscovered Self.
18. Kiersey, D., & Bates, M. (1984). Please Understand Me. Character & Tempperament Types. Del Mar,

California: Prometheus Nemesis Book Company.

19. Lewin, K. (1951). Field Theory in Social Scince; selected theoretical papers. New York, New York:
Harper & Row.

20. Marston, Moulton, & William. (1928). Emotions of Normal People. New York, NY: Harcourt Brace.
21. Mohler, J., & Ritt, T. (1980). Personal Concept. Garwood, New Jersey: Self-Published.
22. Montgomery, S. (2002). People Patterns – A Modern Guide to the Four Temperaments . Archer

Publications.

23. Motley, D., & Hartley, N. (2005). The changing role of personality instruments in assessing behavior in the
classroom. Teaching Economics: Instruction and Classroom-Based Research. Pittsburgh, Pennsylvania:

Society for the Advancement of Management.

24. Munkasey, M. (n.d.). Personality Types, A Commentary on Human Differences. The ISAR International
Society for Astrological Research fil://H:/history.htm

25. Myers-Briggs, I. (1980). Gifts Differing. Palo Alto, California: Consulting Psychologists Press.
26. Personality Insights. (n.d.). Retrieved February 28, 2013, from What is DiSC Personality Test?:

http://www.lifeandleadership.com/personality-test-disc-profile/

27. Powell, R. R. (n.d.). History of Personality Theory. Retrieved from
http://armchair_armchairacademic.homestead.com/HistoryPER ns4.html

28. Ritt, T (1980) Understanding Yourself and Then Others. Ocean, New Jersey, People Concepts
29. Rotter, J. (n.d.). Social Learning Theory. Retrieved from

http://stutzfamily.com/mrstutz/APPsych/psychos/rotter.html

30. Sanderlands, L. E. (n.d.). What is So Practical about Theory? Lewin Revisited. Journal for the Theory of
Social Behavior .

31. Senge, P., Kleiner, A., Roberts, C., Ross, R., & Smith, B. (1994). The Fifth Discipline Fieldbook. New
York, New York: Doubleday Dell Publishing Group, Inc.

32. Staw, B. M. (2004). Psychological Dimensions of Organizational Behavior. Upper Saddle River, New
Jersey: Pearson Education.

33. Tahmincioglu, E. (2011, August 8). Employers turn to tests to weed out job seekers. Retrieved 2012, from
Careers on NBC News: http://www.nbcnews.com/id/44120975/ns/business-

personal_finance/#.USKZa7_6M7A

34. The Benefits of Using DiSC. (n.d.). Retrieved from discprofile: http://www.discprofile.com/what-is-
disc/benefits.htm

35. Thesaurus. (n.d.). Retrieved from http://thesaurus.yourdictionary.com

http://creativecommons.org/licenses/by/3.0/

http://www.cluteinstitute.com/

http://www.lifeandleadership.com/personality-test-disc-profile/

http://armchair_armchairacademic.homestead.com/HistoryPER%20ns4.html

http://stutzfamily.com/mrstutz/APPsych/psychos/rotter.html

http://www.nbcnews.com/id/44120975/ns/business-personal_finance/#.USKZa7_6M7A

http://www.discprofile.com/what-is-disc/benefits.htm

http://thesaurus.yourdictionary.com/

Reproduced with permission of the copyright owner. Further reproduction prohibited without
permission.

IJMRR/ May 2013/ Volume 3/Issue 5/Article No-3/2855-2862 ISSN: 2249-7196

*Corresponding Author www.ijmrr.com 2855

INTERNATIONAL JOURNAL OF MANAGEMENT RESEARCH

AND REVIEW

ORGANIZATIONAL CONFLICT MANAGEMENT STRATEGIES ON EMPLOYEE

JOB SATISFACTION: A CONCEPTUAL RELATIONSHIP

Shehu Aliyu Mukhtar*
1

1
Department of Management Sciences, Kano State College of Arts and Sciences, Kano-

Nigeria.

ABSTRACT

The paper provides a general look at conflict and conflict management strategies in

workplace. As part of its objective, it discovered the common sources and types of conflict,

basic component to conflict, importance as well as problems associated with conflict in an

organizational setting.The paper delves on some aspect of employee job satisfaction. It

proposes anfuture empirical investigation between organizational conflict management

strategies and employee job performance.

Keywords: Conflict management, strategy, organization, workplace.

1. INTRODUCTION

Conflict is as old as man, because it coexists with human existence and interaction between

different social forces (human beings, religion, culture, marriage) that make up the human

society. The social composition of the society reveals the existence of various social elements

which share so many things in common in terms of culture, biological nature; identity and so

on (Veshki, Jazayeri, Shariff, Esfani, Aminjafari&Hosnije, 2012). However, human beings

differs in so many respect as a result of individual differences which manifested in form of

emotional feelings, perception, physical structures, psychology etc. Despite, these differences

the social nature of man necessitates the interaction of man with another fellow human

being(s). However, the more they interact the more there is bound to be a conflict, as a result

of their differences in either personal, family and societal levels, making conflict endemic

and ubiquitous and as well pervasive in every human society past or present, traditional or

modern, simple or complex, and at all levels of the society. Hence conflict is inevitable as all

human societies, communities, organizations and interpersonal relationships experience

conflict at one time or the other in the process of their regular interactions (Bagobiri and

Kassah, 2009). Conflict affects the entire organisation, its segments, sub-segment and

components the same way it affects the society in general.Therefore, conflict is inevitable

between organization and organizational members within the environment, which simply

means that conflict is a common phenomenon between workers and the management and

between individual workers within the organization.

Conflict management may be perceived as a wider concept involving conflict resolution and

transformation when necessitated and it is more of a long term arrangement involving

institutionalized provision and regulative procedures for dealing with conflict. Whenever they

IJMRR/ May 2013/ Volume 3/Issue 5/Article No-3/2855-2862 ISSN: 2249-7196

occur, people must learn to manage conflict productively, otherwise the risk to society and it

development are overwhelming, individual and organization use various approaches to

manage / resolve

conflict.

1.1 Problem Statement

Conflict is inevitable in human society, it arises with human existence. One cannot eliminate

conflict but it can be properly managed. Differences in goal attainment, shared resources,

interdependence in work activities, poor communication, and perception are identified as

major problems leading to organization conflict (Aliyu, 1999). Poorly handled conflict may

generate more conflict at an individual or organizational level (Woodrow, 1999).

2. LITERATURE REVIEW

The concept has been variously defined by different scholar and other stake holders.Robbin

(1974) defined Conflict as any kind of opposition or antagonistic between two or more

parties.Conflict is a fight and contest among people with opposite needs, ideas, beliefs,

values, or goals (The Foundation Coalition, 2003). Zorn (2009) viewed conflict as a state of

affairs in which people express differences in satisfying their needs and interests, and they

experience interference in achieving them. Omolalabi (2001) viewed conflict as a state of

serious disagreement and argument about something perceived to be important by at least one

of the parties involved.Sasso, (1990) defines conflict as a process in which an individual

firmly makes a conversed effort to offset the efforts of another individual by some form of

obstruction that causes hindrance to the latter in accomplishment of his goals or furtherance

of his interests.It is defined as a mere disagreement between two or more organizational

members or groups arising from the fact that they must engage in inter-dependent work

activities and from the fact that they have different status, goals, values and perceptions. Gray

and Sarke (1989) in Bagobiri and Kassah (2009), defined conflict as a behaviour by a person

or group that is purposely designed to inhibit the attainment of goals by another person or

group. Based on this definition, conflict can be seen as a state of opposition, disagreement or

incompatibility between two or more people, group or organization which is sometimes

characterized by physical violence.Wilson and Hanna (1990) describe conflict as a struggle

involving opposing ideas, values, and or limited resources, this shows that conflict exist

between employees and management, where each partly want to achieve the objectives /

goals through scarce resources available in the organization. In a nutshell, conflict is viewed

as an action which presents, obstruct, interferes with, injures or renders ineffective another

action with which it is incompatible.Conflict management involves implementing strategies

to limit the negative aspects of conflict and increase the positive aspects of it at a level equal

to or higher than where the conflict is taking place. The aim of conflict management is to

enhance learning and group outcome (Rahim, 1992). It is not concern with eliminating all

conflict or avoiding it. Conflict can increase group outcome when managed properly. Overall

conflict management should aim to minimize conflict at all levels, attain and maintain a

moderate amount of substantive conflict, and use the appropriate conflict management

strategy to effectively brings about solutions, and also to match the status and concerns of the

parties in conflict. On the other hand, organisation is seen as a system, having an established

structure and conscious planning, in which people work and deal with one another in a

IJMRR/ May 2013/ Volume 3/Issue 5/Article No-3/2855-2862 ISSN: 2249-7196

coordinated and cooperative manner for the accomplishment of recognized goals. In as much

as people will work together in order to achieve stated objective there is bound to be a

conflict.

2.1 Types of Workplace conflict

Workplace conflict is a specific type ofconflict that happens in workplaces. According to

Luthan (1998), conflict can occur at the individual, interpersonal, group or organizational

levels. Kirkwood (2002), viewed the various types of conflict that exist in organizations to

includes data conflicts, structural conflicts, relationship conflicts, and interest conflicts which

can lead to disputes, grievances, lawsuits, complaints, strikes, and disciplinary actions.Rahim

(1992), identified the following workplace conflict types as:

a- Inter-personal Conflict: This is a conflict between two or more individuals due to

personality differences. It arises due to differences in experience and the Knowledge of

carrying out certain task. For instance, conflict may arise between production engineer and

foreman. The engineer who feels he has the knowledge of production, thus processes should

be followed systematically on the other hand, foreman feels that he has the experience and

therefore, some processes should be rejected to minimize cost.

b- Between Individual and group: This type of conflict arises because of the way individuals’

deals with the pressures for conformity imposed on them by their work group; it is the

inconsistencies that arise between individual’s decision and that of the group.

c- Between groups in the same organisation: This is a conflict between Organisations

functional units because of the inter-relationship that existed between them. For instance,

sales department may be in conflict with production department either because quality is too

low or prices are too high to meet with competition.

d- Between organisations in the same Environment: This deals with external to organisations.

It is the existence of conflict between the various organisations within the environment.

2.2 Sources of Conflict in the Work Place

Aliyu (1999), identified five major sources of conflict within the organisational setting as:

• Shared Resources: This potential of conflict exists because vital resources in

organisations are limited, and at the same time such resources need to be allocated. Some

groups will inevitably get less than what they need, therefore conflict arise because

organisational groups compete for the greatest possible share of the limited available

resources.

• Differences in goals: Various functional units within the organisation with dissimilar

goals, know-how and responsibility tend to be in conflict with one another. For instance,

sales department may wish to lower price to attract customer while production department

may wish to increase price to meet with current production costs.

• Interdependence of work activities: the potential for conflict to exist in situations where

two or more sub-units depends upon each other to complete their tasks if the works are

evenly distributed but the rewards are dissimilar

IJMRR/ May 2013/ Volume 3/Issue 5/Article No-3/2855-2862 ISSN: 2249-7196

• Differences in Values, perception and attitudes: Individual differences in values attached

to things and issues, the way and manner through which people perceived things and issues as

well as individual behaviour also result to conflict. Where there are differences in goals

among organisational units, such differences usually result to different attitude, values and

perception and these often lead to conflict.

• Poor Communication: This implies a situation of either preventing others from

understanding an issue or failure to fully and clearly define the duties and responsibility of

individuals and sub-units. Barriers in communication lead to failure to understand and clarify

issues, hence serving as a major source of conflict.

Bell (2002) advocates on the following reasons as the major source for conflict in the

workplace: conflicting needs, conflicting styles, conflicting perceptions, conflicting goals,

conflicting pressures, and conflicting roles.Echezona (2007) identied the following as the

major cause of Conflict which includes among others as; political factors, external factors,

economic factors, government policy, inadequate flow of information sharing, development

patterns/inequalities, ethnic/ religious factors respectively.

2.3 Component of

Conflict

Kaneth (1984), suggested four components in the conflict Process as follows:

a- Parties Involved: Conflict must involve at least two parties i.e. individuals, groups and

organisation.

b- Field of the conflict: The field of conflict is defined by Kaneth as ‘The whole set of

relevant possible state of the social system’. This means any of the parties view would

interfere, intervene or cause friction to itself, work process or the goal of the organisation.

c- Dynamic of the conflict situation: This means that each party adjusts its position, it feels

is congruent to its opponent. It is the level or state of intensity with which the conflict is

pursued or existed over time. One thing to note on the dynamics of conflict is that it

fluctuates over time.

d- Management control/ Resolution of conflict: Whether the field of conflict is justified or

not, the destructive or constructive, the dynamics of conflict cannot be left unable. As conflict

cannot be solved or eliminated once and for all because of its dynamic nature. What is of

importance in conflict resolution is to prevent it from becoming pathological.

2.4 Conflict Management and Control

Conflict management is a process whereby managers in organizations decide on the proper

methods to take in order to manage conflict situations. Whether strategies usedwill entail

overpowering conflict or stimulating it, is usually a matter managers have to decide on by

themselves.Aliyu(1999), identified the following elements as ideal for minimizing and

controlling conflict in organisations work structures and procedures which includes:

• Ensuring that data for problem solving are generated in common: This method involves

the setting up of meetings or task forces with members cutting across various departments

and organisations structure. It also involves hearing from all parties to conflict.

IJMRR/ May 2013/ Volume 3/Issue 5/Article No-3/2855-2862 ISSN: 2249-7196

• Rotating people among the different work group and department in the organisation: This

involves job enrichment most especially job rotation. This can be improve through enhancing

the manpower training of the employees.

• Recognising the interdependence of individuals and groups and establish means of

bringing them into closer contact: This entails coordination and integration aspect of

management functions. Canteens, sporting facilities, parties and other social and recreational

activities promote interaction among staff.

• Locating a common enemy: Conflicting parties may be made to realise that, the conflict

may emanates from a third party and the third party could be inside or outside the

organisation.

• Developing a common set of goals and objectives: These goals and objectives are the

justifiable reasons for organisations existence; therefore, effort should be geared toward

accomplishing them.

• Producing Organisational manuals and handbook: Thorough reading and understanding

of them could improve performance in that they guide workers in performing jobs, spell out

channels of communication, rights and obligations, rewards and penalties.

• Minimising status barriers and Rigidity: Here flexibility should be adapted and review of

rules, procedures, manual instructions and decision should be in harmony with changing

organisational environment.

In (2008), Joshi identified the following as the management strategies in conflict when he

conducted an interview with 74 children between the ages of (8.5-11.5) in an exploratory

study of interpersonal conflict between Children. The management strategies are: submission,

compromise, conventional, standoff, third party intervention, aggression, assertion,

discussion, appeal to a rule, withdrawal. Non-action, adult intervention, and time elapse.

George, et.al (2013), identified the following approaches to conflict management:

• Smoothing mode: In this approach conflict is completely denied. The parties to the

conflict ignore the conflict by putting it under the carpet and pretend that it does not matter or

exist.

• Avoidance / Unilateral Moves: In this case conflict can be resolved when one party

withdraws. This is mostly useful to inter-personal conflicts. It should be clearly understood

that when a party withdraws the other party will no longer be in conflict.

• Edicting/ Placation of Parties Involved: In this approach the conflicting parties are usually

called by higher level administrators and persuaded them so as to reach a consensus.

• Confrontation Mode: At this stage the resolution absolute power is used by the third party

within or outside the organisation. It is however worthy to know that all avenues are

exhausted, proper hiring taken and objective judgement made before resorting to this

approach.

2.5 Importance of Conflict

IJMRR/ May 2013/ Volume 3/Issue 5/Article No-3/2855-2862 ISSN: 2249-7196

Atiomo (2000) cited in Abubakar (2009), identifies the following benefits associated with

conflict in organisational settings as:

• Conflict helps to raise and address Problems: It is through conflict that both manager and

subordinate will be able to identify problems and it is through this, that the problem identified

will be address with a view of providing lasting solution to the problem.

• Energizes workers: Conflict in an organisation lead to energize workers/ employees to

perform certain job/ task, so that organisation can achieve its primary goal, e.g. market share,

profitability, higher sales volume and goodwill.

• Help people learn how to Recognise and benefits from their differences: Human being

differs in many different ways e.g. perception, believe, values and norms, etc. It is through

conflict that most of these differences are identified and people tend to benefit from them.

• Helps Organisation to move forward: It is with conflict that individual differences are

identified which will in the long run pave way for members of such organisation to map out

strategies of overcoming with the major cause of conflict, hence allows for team work and

consequently result in moving the organisation forward. The paper discovered a number of

problems associated with conflict, despite numerous benefits derived from it existence.

2.6 Problems associated with workplace conflict

Management

Carter (2008), identified the following problems:

� Hamper Productivity: Conflict affect organisational productivity because of the simple

fact that little or no attention will be given to the job, thereby concentrating on major issues

that causes the conflict, hence lower productivity is to be achieve.

� Conflict lead to Poor Morale: When conflict exists in an organisation, there are likely

tendencies of having behaviour disorder in that organisation, i.e. issues like disrespect of

supervisors, poor attitude to work, late coming etc.

� Conflict causes more and continued conflict: The existence of conflict in organisational

setting, if not adequately managed and or minimised will serve as an avenue for continued

conflict. Managers are strongly advised to objectively assess conflict situation with a view of

providing lasting solution.

� Conflict lead to Friction of organisational Members: As the name implies, conflict divide

the members of organisation in to a number of groups, each with distinct ideology and goal to

achieve. Hence, the principle of teamwork which is an integral part of management objective

will not be realised.

� Conflict leads to deviation in Goal Attainment: The existence of conflict in organisational

setting, if not adequately managed will lead to failure of achieving the primary goals and

objectives of affected organisations.

2.7 Concept of Job

Satisfaction

Job satisfaction is the feeling of an employee towards his work. Aliyu(1995) describes morale

fromindividuals’ point of view as the degree to which individual needs are satisfied and the

degree to which the individual desires satisfaction from his total job situation Work

satisfaction is an important workplace construct and one that is of concern for effective

IJMRR/ May 2013/ Volume 3/Issue 5/Article No-3/2855-2862 ISSN: 2249-7196

management. Satisfaction is a pleasing or positive demonstrative state resulting from the

appraisal of one’s job (Carter, 2008).Satisfaction with supervision is one of the most

important attitudinal issues in the workplace that managers face. Itis a collection of feelings

or affective responses of the organizational members which are associated with the job

situation within the organization. Individual subordinate with higher levels of satisfaction

with regulation demonstrates lessened propensity to look for other job and decrease

propensity to leave (Judge, Thoresen, Bono & Patton,2001). It is important for managers to

improve ways of satisfying employees.Dana (2001) defined workplace conflict as a

circumstance amongworkers whose jobs are interdependent, who feel annoyed, who perceive

others as being a fault and who act in ways that cause a business problem.

3. PROPOSED RESEARCH FRAMEWORK

Base on the above discussion and literature review, this paper proposes a conceptual

framework illustrated as

The literature reviews indicate a direct relationship between Organizational Conflict

Management Strategies and Employee Job Satisfaction. Hence, the framework suggests that,

the ability of Organization conflict management depends to a large extend on Employee job

satisfaction. The framework could be empirically examined in the future study.

4. CONCLUSION

Conflict represents a mere disagreement between individuals within an organisation. It is as

old as man, meaning there was conflict right from day one. No organisation regardless of its

sound policies, plans, goals articulation is free from conflict. Hence, as an endemic and

inevitable phenomenon, it must be addressed to ensure smooth conduct and continuity of the

organisation and achievement of its designated objective (s). Otherwise, continued conflict

brings organisation to its knee and its eventual collapse as a system.

REFERENCES

Abubakar MA. Effective Conflict Management a Catalyst for Industrial Harmony

and Productivity in Nigeria. A Paper Presented At a Departmental Seminar

Organised by the Research and Academic Development committee, School of

Management Studies, Kano StatPolytechnic held on 3
rd
June, 2009.

Aliyu MS. Conflict and Conflict Resolution in organisation. Kano: The

Triumph newspaper, 1999; 7.

Bagobiri YS, Kassah V..Principles of Management (2
nd
Ed.). Zaria: Enifab

Graphics Press, 2009.

Organizational

Conflict
Management

Strategies

Employee Job

Satisfaction

IJMRR/ May 2013/ Volume 3/Issue 5/Article No-3/2855-2862 ISSN: 2249-7196

Bell D. The Ethical Challenges of International Human Rights Nongovernmental

Organizations, New York and Cambridge: Cambridge University Press 2002.

Carter M. Field Guide to leadership and Supervisors. London: Macmillan Press, 2008.

Dana D. Conflict resolution: mediation tools for everyday worklife. New York: NY:

McGraw-Hills, 2001.

Echezona RI. The role of Libraries in Information Decision for Conflict Resolution,

Peace promotion and reconciation.African Journal of Libraries and Information

Science 2007; 17(2): 153-163.

George GE, Miroga JB, Omweri AN. Organizational Conflict Management

Strategies on Employee Job satisfaction: A Case Study of Nzoia Sugar Company.

European Journal of Business and Management 2010; 5(3): 117-186.

Judge TA, Thoresen CJ, Bono JE, Patton GK. The Job Satisfaction-Job

Performance Relationship: A Qualitative and Quantitative Review. Psychological

Bulletinm 2001; 127(3): 376-407.

Joshi A. Conflict resolution between friends during middle childhood.The Journal of

Genetic Psychology 2008; 169(2): 133-148.

Kaneth EB. A Pure Theory of Conflict Applied to Organisation London.British

Psychological Society and Macmillan Press Ltd, 1984.

Omoluabi PF. Principle and Processes of conflictology. Ife psychologies

International Journal 2001; 9(2): 10-13.

Robbin SP. Managing organizational conflict: A non- traditional approach.

Englewood cliffs, N.J: Prentice-Hall, 1974.

Rahim MA. Managing Conflict in Organisation. West Part, Connecticut, Quarum

Books, 1992.

Veski SK, Jazayeri R, Sharifi E, Esfani SB, Aminjafari A, Hosnije AHS.

Interdisciplinary Journal of Contemporary Research in Business 2012; 4(7): 148-156.

Wilson MO, Hanna B. Management Change: Conflict Negotiation.London:

Longman group ltd, 1990.

Reproduced with permission of the copyright owner. Further reproduction prohibited without
permission.

Turn in your highest-quality paper
Get a qualified writer to help you with

“ Personal Model of Conflict Resolution ”

Get high-quality paper

NEW! AI matching with writer

Still stressed with your coursework?

Get quality coursework help from an expert!

Order now