The following image is the payoff matrix of two prisoners, Bonnie and Clyde, in a jail suspected of a bank robbery. They are placed in separate cells in the county jail and are not allowed to talk with each other. Suppose Bonnie and Clyde both pursue their own self-interest in a noncooperative game. Which of the following is the most likely outcome of the game?Figure 9.4:

Question

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This is a classic example of the prisoner's dilemma, where each prisoner has the option to either confess (betray) or remain silent (cooperate). Since they are not allowed to communicate with each other, they cannot coordinate their actions, and each must make a decision based solely on their own self-interest. In this case, both prisoners have a dominant strategy to confess regardless of what the other does because it gives them the best outcome.

Suppose Bonnie confesses and Clyde remains silent, then Bonnie goes free, and Clyde gets 20 years in jail. If Clyde confesses and Bonnie remains silent, then Clyde goes free, and Bonnie gets 20 years in jail. If both confess, then they both spend 8 years in jail, and if both remain silent, they both spend 1 year in jail.

Therefore, the most likely outcome of the game is that both will confess, and they both will spend 8 years in jail. Thus, choice A) "Both spend 8 years in jail" is the best choice.

The Following Image Is the Payoff Matrix of Two Prisoners