Consider the prisoner's dilemma game, in which two prisoners are accused of a crime. Both are isolated in the prison. Without a confession, there is not enough evidence to convict either. Any prisoner who confesses will be looked upon with lenience. If one prisoner confesses and the other does not, that prisoner not confessing will be put away for a much longer sentence. The payoffs can be represented as pictured in Figure 14.7 (Player 1's payoffs are in the upper right, and Player 2's are in the lower left).
a. Determine the Nash equilibrium strategy for each player. What would be the result of the game if both players chose this strategy?
b. In most experiments involving the prisoner's dilemma, we observe that players tend to choose not to defect a reasonable proportion of the time. How might this be motivated by altruism?
c. If a selfish player is playing the prisoner's dilemma against an opponent she believes to be altruistic, what would her strategy be? Is this similar to the observation in the TIOLI game? Why or why not?
d. Now suppose that the prisoner's dilemma is played three times in sequence by the same two players. How might a belief that the other player is altruistic affect the play of a selfish player? Is this different from your answer to c? What has changed?