Consider an infinitely repeated oligopoly game between two firms. While in class
ID: 2495308 • Letter: C
Question
Consider an infinitely repeated oligopoly game between two firms. While in class we discussed a model of quantity competition, now assume that the two firms compete by setting prices. In other words, the stage game of this repeated game is a Bertrand price competition game. Recall that in the Bertrand game consumers purchase only from the firm with the lowest price and if both firms charge the same price each obtains half of the market demand. For this exercise assume that the direct market demand is: Q = 14 - p (where p is the lowest price) and that each firm has a marginal (or per-unit) cost of 2 dollars. The monopoly price in this market is 8. What is the cooperative payoff u_i^c? Assume firms can only set integer prices. What is the deviator's payoff u_i^d? What is the punishment payoff u_i^p?Explanation / Answer
a. If they cooperate, then the price can be set at 8. Then Q will be 14-8=6.
Revenue per firm = 8*6/2
= 24.
b. If a firm sets $6 as its price and the other remains at $8, then Q = 14 - 6,
Q=8; revenue will be 8*6 = 48 which will be taken by a single firm.
c. Punishment payoff, their price would be MC. Just like in perfect competition.
Revenue per firm = 12*2/2
= 12.