Suppose that the Prisoners’ Dilemma stage game is repeated for infinitely many periods.

Suppose that the Prisoners’ Dilemma stage game is repeated for infinitely many periods.

a. Can players support the cooperative outcome by using tit-for-tat strategies, punishing deviation in a past period by reverting to the stage-game Nash equilibrium for just one period and then returning to cooperation? Are two periods of punishment enough?

b. Suppose players use strategies that punish deviation from cooperation by reverting to the stagegame Nash equilibrium for ten periods before returning to cooperation. Compute the threshold discount factor above which cooperation is possible on the outcome that maximizes the joint payoffs.