4 Question – Repeated Duopoly

4 Question – Repeated Duopoly
Now he have exactly the same problem as before, a duopoly with
same demand curve, identical cost structure for both firm A and B,
but now they are going to play the game repeatedly infinitely.
Assume they are both have the same discount rate for future payoffs
.
a) Now they decide to collude and to chose in every period the
quantity that maximizes the overall profit in one period. Which
quantity they will produce, what will be the final price and the
profit each will get (assume they will split the collusion profit
equally).
b) If they are competing via Bertrand style and Firm A decides
to break the agreement what profit would firm A get?
c) If they are competing via Cournot style and Firm A decides to
break the agreement what profit would firm A get?
d) Assume now they are playing infinitely and each firm is using
the trigger strategy1. What is the minimum discount rate that
can sustain the collusion as a SPNE if the are competing via
Bertrand? What if the are competing via Cournot?