Two players play an asymmetric prisoner’s dilemma

or Defect. The payoffs from each pure strategy profile are as follows: for (c, c), (2, 4); for (c, d), (0, 5); from (d, c), (4, 0); from (d, d), (1, 1).1 This stage game is repeated infinitely many times. Players seek to maximize the discounted sum of their payoffs. They have a common discount factor δ.

(a) Show conditions on δ such that there is a subgame perfect Nash equilibrium (SPNE) of the repeated game in which both players cooperate in every period.

(b) According to the Folk Theorem, is there an SPNE in which the players alternate between playing (c, d) and (d, c) in every period?

1Strategy pairs list the action of player 1 first. Payoff pairs list the payoff of player 1 first.

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