The dynamics of deterrence.

Because punishment is scarce, costly, and painful, optimal enforcement strategies will minimize the amount of actual punishment required to effectuate deterrence. If potential offenders are sufficiently deterrable, increasing the conditional probability of punishment (given violation) can reduce the amount of punishment actually inflicted, by "tipping" a situation from its high-violation equilibrium to its low-violation equilibrium. Compared to random or "equal opportunity" enforcement, dynamically concentrated sanctions can reduce the punishment level necessary to tip the system, especially if preceded by warnings. Game theory and some simple and robust Monte Carlo simulations demonstrate these results, which, in addition to their potential for reducing crime and incarceration, may have implications for both management and regulation.