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.crime ͉ enforcement ͉ game theory ͉ positive feedback ͉ tipping H umans cooperate; the extent of cooperation among humans marks them out from all other species (1, 2). But cooperation is vulnerable to exploitation through aggression, deception, opportunistic defection from agreements, and free-riding. Where cooperative strategies are suboptimal for individuals, mutually beneficial arrangements will fail to arise, or will degenerate (3-5).Under experimental conditions, some individuals will voluntarily incur costs to themselves to punish noncooperative behavior; doing so can facilitate cooperation by reducing the potential gains from exploitation (1, 4, 6). Thus punishment is a basic element of human social interaction.As punishment is always costly, both to the punisher and (obviously) to those punished, a well-designed enforcement system should combine high efficacy in discouraging exploitative behavior with low actual infliction of sanctions. At first blush, it might seem that these 2 objectives are in fundamental tension; that more compliance requires more punishment. But 3 law-enforcement examples seem to support the contrary proposition.First, when the New York City Police Department implemented a ''zero tolerance'' policy toward ''squeegeeing''-penny-ante extortion involving wiping the windshields of cars stuck in traffic and then ''requesting'' payment from the drivers-by arresting every squeegee-man observed plying his trade, the number of actual arrests for squeegeeing went down, not up (7). The same happened when the New York City Transit Police cracked down on ''turnstile-jumping.'' Second, police in High Point, NC, who had been sporadically arresting drug dealers in a long-established crack market for 2 decades and finding that every arrestee was quickly replaced, changed strategies. They identified all of the currently active dealers in that market and developed felony cases against them, but arrested and prosecuted only 3 dealers who had been involved in violence. They then held a meeting with the remaining dealers and announced that anyone who continued to sell drugs would face certain prison time. Soon after, the market disappeared, and the number of crack-deali...