Crime, punishment, and evolution in an adversarial game

Abstract

We examine the game theoretic properties of a model of crime first introduced by Short et al. (2010 Phys. Rev. E82, 066114) as the SBD Adversarial Game. We identify the rationalizable strategies and one-shot equilibria under multiple equilibrium refinements. We further show that SBD's main result about the effectiveness of defecting-punishers (“Informants”) in driving the system to evolve to the cooperative equilibrium under an imitation dynamic generalizes to a best response dynamic, though only under certain parameter regimes. The nature of this strategy's role, however, differs significantly between the two dynamics: in the SBD imitation dynamic, Informants are sufficient but not necessary to achieve the cooperative equilibrium, while under the best response dynamic, Informants are necessary but not sufficient for convergence to cooperation. Since a policy of simply converting citizens to Informants will not guarantee success under best response dynamics, we identify alternative strategies that may help the system reach cooperation in this case, e.g., the use of moderate but not too severe punishments on criminals.

Bribery games on interdependent complex networks

“…Firstly, such a game provides a realistic model to explore the effects of punishment on reducing corruption and enabling ethical behaviour. Several recent studies (D'Orsogna et al, 2013;D'Orsogna and Perc, 2015;Helbing et al, 2010;Lee et al, 2017Lee et al, , 2015McBride et al, 2016;Rand and Nowak, 2011;Short et al, 2010;Sigmund, 2007;Perc, 2013a, 2015) have begun to address the impact of punishment and reward on deterring criminal behaviour in mixed as well as structured populations. Such social conflicts characterized by competing interests and distinct strategies of interacting players also provides a natural framework for analysing evolutionary game dynamics on 3 interdependent networks.…”