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 that the role played by penalties in mixed strategy equilibria is fundamentally different from the role they play in pure strategies. We also identify sufficient conditions for the implementability and uniqueness of given equilibria when there are restrictions on the penalties and/or on the incentive schemes for the law enforcers. Finally, we give a rationalization for the use of mixed strategies as a solution concept in law enforcement games.