Question

Suppose that two players play an infinite-horizon Prisoner’s Dilemma game, with discount factor δ > 0. The

payoffs during each stage of the game are given below

Player 1 has two strategies: {C,D) and Player 2 has two strategies (C,D)

(C,C) = (1,1), (C,D) = (-4,4), (D,C) = (4. -4) and (D,D) = (0,0)

If player 1 receives the payoff pk in stage k then Player 1’s total payoff in the repeated game is p1 + δp2 + δ2p3 +··· Similarly, if Player 2 receives the payoff qk in stage k then player 2’s total payoff is q1 + δq2 + δ2q3 +···

Find the conditions on the discount factor δ such that cooperation can be supported in the infinitely repeated game

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