Abstract
As a simple model for criminal behavior, the traditional two-strategy inspection game yields counterintuitive results that fail to describe empirical data. The latter shows that crime is often recurrent, and that crime rates do not respond linearly to mitigation attempts. A more apt model entails ordinary people who neither commit nor sanction crime as the third strategy besides the criminals and punishers. Since ordinary people free-ride on the sanctioning efforts of punishers, they may introduce cyclic dominance that enables the coexistence of all three competing strategies. In this setup ordinary individuals become the biggest impediment to crime abatement. We therefore also consider heterogeneous punisher strategies, which seek to reduce their investment into fighting crime in order to attain a more competitive payoff. We show that this diversity of punishment leads to an explosion of complexity in the system, where the benefits and pitfalls of criminal behavior are revealed in the most unexpected ways. Due to the raise and fall of different alliances no less than six consecutive phase transitions occur in dependence on solely the temptation to succumb to criminal behavior, leading the population from ordinary people-dominated across punisher-dominated to crime-dominated phases, yet always failing to abolish crime completely.
Highlights
As a simple model for criminal behavior, the traditional two-strategy inspection game yields counterintuitive results that fail to describe empirical data
We can conclude that the real obstacle in the fight against criminal behavior is the possibility of ordinary people to free-ride on the efforts of punishers
We have studied the effectiveness of punishment in abating criminal behavior in the spatial inspection game with three and five competing strategies, entailing criminals, ordinary people and punishers
Summary
As a simple model for criminal behavior, the traditional two-strategy inspection game yields counterintuitive results that fail to describe empirical data. One broken window is likely to become many broken windows, and the inception of urban decay and criminal behavior is in place The simplicity of this widely adopted criminological theory invites mathematicians and physicists to adopt a complex systems approach[6] to study criminal behavior[7], in particular since the collective behavior of the system in this case can hardly be inferred from the relatively simple individual actions. Emergent phenomena such as pattern formation including percolation[8,9] and phase transitions are commonly associated with complex social and biological systems[10,11,12,13], and in this realm the mitigation of crime is certainly no exception. Simulations have revealed that in the realm of the adversarial game informants are key to the emergence of a crime-free society, and this has subsequently been confirmed with human experiments[32]
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