Crime, Punishment, and Evolution in an Adversarial Game

We examine the game theoretic properties of a model of crime first introduced by Short, Brantingham, and D'Orsogna (Short et al. 2010) as the SBD Adversarial Game. We identify the rationalizable strategies and one-shot equilibria under mul- tiple equilibrium refinements. We further show that SBD's main result about the effectiveness of defecting-punishers in driving the system to evolve to the cooperative equilibrium under an imitation dynamic does generalize to a best response dynamic, although the nature of this strategy's role differs significantly between the two dynamics. The analysis reveals that the positive externality in punishing crime in the SBD game converts the adversarial setting from a social dilemma to a coordination game. We provide policy implications and lessons learned about the evolution of cooperation more generally.