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There is a rough neighborhood with n¡Ý 2 residents. Each resident has to ecide whether to engage in the crime of theft. If an individual chooses to be a thief and is not caught by the police, he receives a payoff of W. If he is caught by the police, his payoff is Z. If he chooses not t commit theft, he receives a zero payoff. Assume that W > 0 > Z. All n residents simultaneously decide whether or not to commit theft. The probability of a thief being caught equals 1 over m, where m is the number of residents who choose to engage in theft. Thus, the probability of being caught is lower when more crimes are committed and the police have more crimes to investigate. The payoff from being a thief, given that m-1 other people have also chosen to be thieves, is then
(m-1) W +(1)Z
m m
Find all Nash Equilibrium
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