Only two identical firms i = A;B, each with marginal cost MCi = 40 and no fixed cost, operate in a market with demand:
Q p
1 160
2 120
3 90
4 70
5 50
6 40
(a) Suppose that the firms select simultaneously the quantities they wish to produce. Obtain the normal form (payout table) representation of this game and determine the Nash equilibria (Cournot solution). Also obtain the collusive allocations, in which firms maximize joint profits, and the socially efficient allocations.
(b) Suppose that the firms meet again one more time in the future, selecting their quantities simultaneously in each period (as in part (a)) but observing each others first period choices before the second period market takes place. Which is the perfect equilibrium of the corresponding twice repeated game? What if they interact repeatedly for ten periods? Explain.
(c) Suppose that the firms continue to interact indefinitely over time; having at each period a probability equal to 0:75 of meeting again for at least one more period. Can the collusive solution be supported as a Nash equilibrium of this repeated game? If so, describe the corresponding equilibrium strategies.