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Stochastic evolutionary selection in finite populations

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  • Zhang, Yanfang
  • Mei, Shue
  • Zhong, Weijun

Abstract

We primarily focus on a wide range of stochastic evolutionary game dynamics between two strategies which are characterized by a condition we call monotonicity: the sign of the difference between the probabilities of increasing and decreasing an A-individual completely depends on the difference of payoffs based on different strategies. When mutations are excluded, we provide sufficient conditions for selection to favor one strategy over the other and necessary conditions for selection to favor or oppose change, respectively. Moreover, we discuss which strategy will be favored in case of rare mutations and give a simple rule to determine evolutionary selection of strategies for large populations under some specific stochastic mutation–selection dynamics.

Suggested Citation

  • Zhang, Yanfang & Mei, Shue & Zhong, Weijun, 2011. "Stochastic evolutionary selection in finite populations," Economic Modelling, Elsevier, vol. 28(6), pages 2743-2747.
    • Handle: RePEc:eee:ecmode:v:28:y:2011:i:6:p:2743-2747
    DOI: 10.1016/j.econmod.2011.08.017
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    References listed on IDEAS

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    1. Bruckner, E & Ebeling, W & Jimenez Montano, M.A. & Scharnhorst, A., 1996. "Nonlinear Stochastic Effects of Substitution--An Evolutionary Approach," Journal of Evolutionary Economics, Springer, vol. 6(1), pages 1-30, February.
    2. Michel BenaÔm & J–rgen W. Weibull, 2003. "Deterministic Approximation of Stochastic Evolution in Games," Econometrica, Econometric Society, vol. 71(3), pages 873-903, May.
    3. Saviotti, P P & Mani, G S, 1995. "Competition, Variety and Technological Evolution: A Replicator Dynamics Model," Journal of Evolutionary Economics, Springer, vol. 5(4), pages 369-392, December.
    4. Ania, Ana B., 2008. "Evolutionary stability and Nash equilibrium in finite populations, with an application to price competition," Journal of Economic Behavior & Organization, Elsevier, vol. 65(3-4), pages 472-488, March.
    5. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    6. Sandholm, William H., 2005. "Excess payoff dynamics and other well-behaved evolutionary dynamics," Journal of Economic Theory, Elsevier, vol. 124(2), pages 149-170, October.
    7. 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.
    8. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-666, May.
    9. Fudenberg, Drew & Imhof, Lorens A., 2006. "Imitation processes with small mutations," Journal of Economic Theory, Elsevier, vol. 131(1), pages 251-262, November.
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    More about this item

    Keywords

    Stochastic evolutionary game dynamics; Finite populations;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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