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Crime, punishment, and evolution in an adversarial game†

Published online by Cambridge University Press:  21 December 2015

MICHAEL MCBRIDE ,
RYAN KENDALL ,
MARIA R. D'ORSOGNA  and
MARTIN B. SHORT
MICHAEL MCBRIDE
Affiliation:
Department of Economics, University of California, Irvine, CA, USA email: mcbride@uci.edu
RYAN KENDALL
Affiliation:
Department of Economics, University of Southern California, Los Angeles, CA, USA email: rakendal@usc.edu
MARIA R. D'ORSOGNA
Affiliation:
Department of Mathematics, California State University, Northridge, CA, USA email: dorsogna@csun.edu
MARTIN B. SHORT*
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA, USA email: mbshort@math.gatech.edu
*
‡Corresponding author. 686 Cherry Street, Atlanta, GA, 30332-0160, USA, mbshort@math.gatech.edu.
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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. 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.

Keywords

adversarial game theorymathematical criminologysocial modelingbest response dynamicscooperative behavior
Type
Papers
Information
European Journal of Applied Mathematics , Volume 27 , Issue 3: Mathematical Modelling of Crime and Security , June 2016 , pp. 317 - 337
Copyright
Copyright © Cambridge University Press 2015 

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Footnotes

†

The material herein is based upon work supported by the Army Research Office Award No. #W911NF-11-1-0332. McBride and Short were also supported by the Air Force Office of Scientific Research Award No. FA9550-10-1-0569.

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