Penalty and crime with lumpy choices: some further considerations

This paper clarifies an issue in the Hirshleifer and Rasmusen-Tsebelis controversy on the effects of penalties on crime: what is the effect of penalties if the transgression of law has a discrete nature and if the law enforcer cannot act as Stackelberg leader? We differentiate between technical (compliance costs) and institutional (penalties) parameters in the potential transgressor's payoff's functions. Depending on the penalty structure, we obtain equilibria either in pure or in mixed strategies. We confirm Hirshleifer and Rasmusen's results that small changes in the fine structure do not affect the equilibrium that is obtained, but that large changes do. In the equilibria with mixed strategies, we confirm Tsebelis's results that changes in the penalties do affect the potential's transgressor's strategies, but without affecting the probability that the individual chooses a particular element in the support of his strategies.