Cooperation & Trigger Strategies

Question 1.

Two firms are playing an infinitely-repeated prisoner's dilemma pricing game of the following form:
  Firm 2
  lowhigh
Firm 1low  5 ,  5 20 ,  0
high  0 , 20 10 , 10
The firms simultaneously set prices at regular intervals. In the equilibrium of this game, each firm selects the low price. While the equilibrium results in profits of $5 for each firm, collusion can potentially result in payoffs of $10. The firms utilize trigger strategies in order to maintain the collusive outcome.

Suppose that both firms adopt the grim trigger strategy. They continue colluding until one of them cheats. Upon one of them defecting, they play the equilibrium strategy for the rest of the game. What has to be true about the interest rate (r) for collusion to be sustainable?

Question 2.

In the game from question 1, suppose that both firms adopt a tit-for-tat strategy. They initially collude. In future periods, a firm colludes if its competitor did in the previous period, and elects the lower price if its competitor cheated in the previous period. What has to be true about the interest rate (r) for collusion to be sustainable?




see solutions