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A Mathematical Analysis of the Long-run Behavior of Genetic Algorithms for Social Modeling

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  • Waltman, L.
  • van Eck, N.J.P.
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    Abstract

    We present a mathematical analysis of the long-run behavior of genetic algorithms that are used for modeling social phenomena. The analysis relies on commonly used mathematical techniques in evolutionary game theory. Assuming a positive but infinitely small mutation rate, we derive results that can be used to calculate the exact long-run behavior of a genetic algorithm. Using these results, the need to rely on computer simulations can be avoided. We also show that if the mutation rate is infinitely small the crossover rate has no effect on the long-run behavior of a genetic algorithm. To demonstrate the usefulness of our mathematical analysis, we replicate a well-known study by Axelrod in which a genetic algorithm is used to model the evolution of strategies in iterated prisoner’s dilemmas. The theoretically predicted long-run behavior of the genetic algorithm turns out to be in perfect agreement with the long-run behavior observed in computer simulations. Also, in line with our theoretically informed expectations, computer simulations indicate that the crossover rate has virtually no long-run effect. Some general new insights into the behavior of genetic algorithms in the prisoner’s dilemma context are provided as well.

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    Bibliographic Info

    Paper provided by Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam in its series ERIM Report Series Research in Management with number ERS-2009-011-LIS.

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    Date of creation: 09 Mar 2009
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    Handle: RePEc:ems:eureri:15181

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    Related research

    Keywords: economics; evolutionary game theory; genetic algorithm; long-run behavior; social modeling;

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    References

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    12. Floortje Alkemade & Han Poutré & Hans Amman, 2006. "Robust Evolutionary Algorithm Design for Socio-economic Simulation," Computational Economics, Society for Computational Economics, vol. 28(4), pages 355-370, November.
    13. Arifovic, Jasmina, 1996. "The Behavior of the Exchange Rate in the Genetic Algorithm and Experimental Economies," Journal of Political Economy, University of Chicago Press, vol. 104(3), pages 510-41, June.
    14. Marks, R E, 1992. "Breeding Hybrid Strategies: Optimal Behaviour for Oligopolists," Journal of Evolutionary Economics, Springer, vol. 2(1), pages 17-38, March.
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    16. 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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