Penalty has no Impact on Crime:

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Abstract
Existing approaches consider crime as either the consequence of antecedent social conditions or the outcome of a rational calculation by a predator who chooses crime as a utility-maximizing career. Consequently, these approaches propose either an improvement in social conditions or an increase in penalties as a means to reduce criminal activity. This article adopts a game-theoretic framework and examines crime as a game between criminals and the police. On realistic grounds, this approach represents an improvement on the conventional economic analysis of crime, concluding that under a wide variety of conditions (described by axioms 1 through 4), an increase in the severity of the penalty has no impact on criminal behavior at equilibrium. In fact, an increase in the penalty reduces the frequency of law enforcement at equilibrium. The major policy implication is that in order to reduce criminal activity at equilibrium, one has to modify the payoff structure of the police. Several variations of the model are examined.