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Crime, punishment, and evolution in an adversarial game

Mcbride, Michael; Kendall, Ryan; D'Orsogna, MariaR; Short, MartinB; (2016) Crime, punishment, and evolution in an adversarial game. European Journal of Applied Mathematics , 27 (03) pp. 317-337. 10.1017/S0956792515000649. Green open access

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Abstract

We examine the game theoretic properties of a model of crime first introduced by Short et al. (2010 Phys. Rev. E 82, 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.

Type: Article
Title: Crime, punishment, and evolution in an adversarial game
Open access status: An open access version is available from UCL Discovery
DOI: 10.1017/S0956792515000649
Publisher version: http://dx.doi.org/10.1017/S0956792515000649
Language: English
Additional information: © Cambridge University Press 2015.This article has been published in a revised form in European Journal of Applied Mathematics http://dx.doi.org/10.1017/S0956792515000649. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works.
Keywords: Adversarial game theory, mathematical criminology, social modeling, best response dynamics, cooperative behavior
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL SLASH
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of S&HS
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of S&HS > Dept of Economics
URI: https://discovery.ucl.ac.uk/id/eprint/1539043
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