Question

3. a) We know that the single shot prisoner’s dilemma game result in a dominant Nash equilibrium strategy that is Pareto inefficient. Suppose we let the two prisoners talk before the start of the game. Would that change the final outcome of the game? Justify your answer.

b) With a two player, 2 outcome example, explain how a sequential game might have different outcomes depending on when it ends.

Answer 1

3 (a) No it will not change the outcome of the game. Both the players can talk before the game and decide to play the remain silent (do not betray) strategy. But, both will have the incentive to deviate from the strategy once the game starts as deviating to betray gives them a higher payoff. Thus, cooperation before the game is noncredible.

(b) The sequential game can give the (do not betray, do not betray) Nash equilibrium only when the game is player infinitely many times. Both the players can then play tit for tat strategy and it will ensure cooperation to Pareto efficient equilibrium where both players do not confess. Any game played a limited number of times, say n, will again lead to the inefficient outcome as by backward induction in the period n-1, both have an incentive to deviate. But by that logic both will have an incentive to deviate in n-2 as well and so on and so forth such that a finite game cna not solve the inefficieny problem of Prisonners' Dillema.