The following game is a version of the Prisoners€™ Dilemma, but the payoffs are slightly different than in Table.

Prisoners€™ Dilemma in Normal Form

a. Verify that the Nash equilibrium is the usual one for the Prisoners€™ Dilemma and that both players have dominant strategies.
b. Suppose the stage game is played an indefinite number of times with a probability g the game is continued to the next stage and 1 €“ g that the game ends for good. Compute the level of g that is required for a sub game-perfect equilibrium in which both players play a trigger strategy where both are Silent if no one deviates but resort to a grim strategy (that is, both play Confess forever after) if anyone deviates to Confess.
c. Continue to suppose the stage game is played an indefinite number of times, as in b. Is there a value of g for which there exists a sub game perfect equilibrium in which both players play a trigger strategy where both are Silent if no one deviates but resort to tit-for-tat (that is, both play Confess for one period and go back to Silent forever after that) if anyone deviates to Confess? Remember that g is a probability, so it must be between 0 and1.

Transcribed Image Text:

Confess Silent Confess 0,0 3,-1 Silent1, 1 Confess Silent 3,-31,-10 Confess Silent 10,-1 2,-2