Bill and Joe have committed a crime for which the police are questioning them se

Question

Bill and Joe have committed a crime for which the police are questioning them separately. The police tell each of them that if one person confesses and the other does not, the “confessor” will go free in return for cooperating, but the one who doesn’t confess will receive a 20-year sentence. If they both confess, then they will both get 5-year sentences. If neither of them confesses, the police only have evidence to convict them both for a 2-year sentence. Think of Bill and Joe as players of a game where each player has two strategies: “Confess” and “Don’t Confess.” Assume that Bill and Joe both expect to live for 30 more years and will never commit another crime, so that their payoffs are the number of years they will be able to live out of prison (30 minus their prison sentence). The payoff matrix for this “prisoners’ dilemma” game is attached

Explanation / Answer

The payoff matrix will be as follows -

Bill is Row Player and Joe is Column Player -

Best of Luck :)

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