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Crime, Punishment, and Evolution in an Adversarial Game

Author

Listed:
  • Michael McBride

    (Department of Economics, University of California-Irvine)

  • Ryan Kendall

    (Department of Economics, University of California-Irvine)

  • Martin B. Short

    (Department of Mathematics, University of California-Los Angeles)

  • Maria R. D'Orsogna

    (Department of Mathematics, California State University-Northridge)

Abstract

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.

Suggested Citation

  • Michael McBride & Ryan Kendall & Martin B. Short & Maria R. D'Orsogna, 2012. "Crime, Punishment, and Evolution in an Adversarial Game," Working Papers 121308, University of California-Irvine, Department of Economics.
  • Handle: RePEc:irv:wpaper:121308
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    File URL: https://www.economics.uci.edu/files/docs/workingpapers/2012-13/mcbride-08.pdf
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    References listed on IDEAS

    as
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    6. Simon Gachter & Ernst Fehr, 2000. "Cooperation and Punishment in Public Goods Experiments," American Economic Review, American Economic Association, vol. 90(4), pages 980-994, September.
    7. Takahashi, Satoru, 2010. "Community enforcement when players observe partners' past play," Journal of Economic Theory, Elsevier, vol. 145(1), pages 42-62, January.
    8. Eaton, B.Curtis & Wen, Jean-François, 2008. "Myopic deterrence policies and the instability of equilibria," Journal of Economic Behavior & Organization, Elsevier, vol. 65(3-4), pages 609-624, March.
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    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Prateek Verma & Supratim Sengupta, 2015. "Bribe and Punishment: An Evolutionary Game-Theoretic Analysis of Bribery," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-22, July.

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    More about this item

    Keywords

    Cooperation; Punishment; Evolution;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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