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A Model-to-Model Analysis of the Repeated Prisoners’ Dilemma: Genetic Algorithms vs. Evolutionary Dynamics

In: Artificial Economics

Author

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  • Xavier Vilà

    (Universitat Autònoma de Barcelona)

Abstract

We study the properties of the well known Replicator Dynamics when applied to a finitely repeated version of the Prisoners’ Dilemma game. We characterize the behavior of such dynamics under strongly simplifying assumptions (i.e. only 3 strategies are available) and show that the basin of attraction of defection shrinks as the number of repetitions increases. After discussing the difficulties involved in trying to relax the “strongly simplifying assumptions” above, we approach the same model by means of simulations based on genetic algorithms. The resulting simulations describe a behavior of the system very close to the one predicted by the replicator dynamics without imposing any of the assumptions of the analytical model. Our main conclusion is that analytical and computational models are good complements for research in social sciences. Indeed, while on the one hand computational models are extremely useful to extend the scope of the analysis to complex scenarios hard to analyze mathematically, on the other hand formal models can be extremely useful to verify and to explain the outcomes of computational models.

Suggested Citation

  • Xavier Vilà, 2009. "A Model-to-Model Analysis of the Repeated Prisoners’ Dilemma: Genetic Algorithms vs. Evolutionary Dynamics," Lecture Notes in Economics and Mathematical Systems, in: Cesáreo Hernández & Marta Posada & Adolfo López-Paredes (ed.), Artificial Economics, chapter 0, pages 237-244, Springer.
    • Handle: RePEc:spr:lnechp:978-3-642-02956-1_19
    DOI: 10.1007/978-3-642-02956-1_19
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    References listed on IDEAS

    as
    1. Binmore, Kenneth G. & Samuelson, Larry, 1992. "Evolutionary stability in repeated games played by finite automata," Journal of Economic Theory, Elsevier, vol. 57(2), pages 278-305, August.
    2. Martin A. Nowak & Akira Sasaki & Christine Taylor & Drew Fudenberg, 2004. "Emergence of cooperation and evolutionary stability in finite populations," Nature, Nature, vol. 428(6983), pages 646-650, April.
    3. Miller, John H., 1996. "The coevolution of automata in the repeated Prisoner's Dilemma," Journal of Economic Behavior & Organization, Elsevier, vol. 29(1), pages 87-112, January.
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    More about this item

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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