Kleiman, M., & Kilmer, B. (2009)
Kleiman and Kilmer utilize game theory to simulate and analyze two different methods of punishment application (random sanctioning and dynamic concentration) in order to determine which method provides the greatest deterrence to potential violators. The authors state that when rule-breaking is punished more consistently, violations decrease and it is less likely that the threatened punishment will occur, i.e, the deterrence was successful.
In applying the standard rational actor assumption of game theory , the authors test compliance games with one and n potential offenders. In these games, breaking a rule results in payment of penalty P, whereas compliance results in a cost of C. According to the authors, “a rational subject will never violate if the penalty for breaking the rule is above the cost of compliance or gain from violation” (p. 14231). In other words, when P > C, the violation will not occur. In this situation, increasing the severity of the punishment will result in less punishment being used. However, if the punishment is not certain and there is instead a probability of being punished p, then the rule will be broken if and only if pP < C, where the critical value is the probability of punishment. Below that critical value, violations will be consistent, but above that value, violations will be zero. In this situation, increasing the probability of punishment decreases the amount of actual punishment used.
In the next scenario, there are n potential offenders, but less sanctions than players. The first game involves two players who act sequentially (Actor 2 (A2) knows what action Actor 1 (A1) took), only a single available punishment which is randomly assigned, and P > C. If only one player violates, he is punished with certainty, whereas is both players violate, they both have a 50% chance of punishment expected cost of punishment is P/2 (which is assumed to be less than C). Therefore, “comply-comply” and “violate-violate” are both Nash equilibriums. A1 chooses between complying at C or violating at P/2 < C, and because he is rational, he violates and therefore so does A2. Generalized to n players, as long as P/n < C, all will violate. If capacity to punish is increased and made public, where both A1 and A2 know they will be punished, then both actors comply.
The next game changes the punishment from random to a priority assignment on A1. In this situation, A1 will comply because he knows that he, being the highest priority actor, will certainly be punished. Therefore, A2 also complies, because if A1 complies then priority shifts to the next actor. Even if moves are simultaneous instead of sequential, the directly-threatened player will always comply, and therefore so will the rest of the field. In this scenario, regardless of the number of players, the only Nash equilibrium is universal compliance. The authors provide an example of the Texas Ranger with a single bullet in his revolver who prevents an angry mob from rushing the jail by threatening to shoot the first person who steps forward. If no one steps forward, no one is shot, and the jail is not mobbed.
The authors conduct simulations where random sanctions and dynamic concentration are applied to violators in a limited number. In these simulations, as the number of available sanctions increases, the number of violations decrease, regardless of the method of punishment. However, when dynamic concentration is applied, or an offender is given priority, the enforcers “tip” the system from high-violation to the low-violation equilibrium with fewer sanctions than random sanctioning. Increasing the probability of sanctions dramatically increases the advantage of dynamic concentration. In a stochastic world where a single penalty will not deter all offenders, establishing a priority of sanctions reduces violation rates and economizes sanctions.
The authors argue that applying dynamic concentration to groups could continue the current decrease in crime rates while reversing the decades-long prison-building boom that has lead to the US having the world’s highest rate of incarceration per capita. These principles also extend beyond criminal justice to managers, teachers, parents, and others, but may have limited applicability to armed conflict or organized insurgency.
The incorporation of game theory into deterrence makes sense utilizing rational actors; however, the authors mention that dynamic concentration can be defeated when players are allowed to communicate and collude, which occurs in the real world. Additionally, they mention that dynamic concentration would reduce the severity of the punishment that would also “tip” high-violation equilibrium to a low-violation equilibrium, and while I agree that it would likely do so, I do not believe it would be as dramatic as they state. In short, I believe that while dynamic concentration would likely be effective as a deterrent, it would need to be modified to each population that it is applied against, which complicates the strategy.
Source:Kleiman, M., & Kilmer, B. (2009). The dynamics of deterrence. Proceedings of the National Academy of Sciences of the United States of America (PNAS), 106(34), 14230-14235.