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Strictly Dominated Strategies in the Replicator-Mutator Dynamics

Author

Listed:
  • Segismundo S. Izquierdo

    () (Department of Industrial Organization, Universidad de Valladolid, Valladolid, 47011 Spain
    Social Systems Engineering Centre (InSiSoc), Valladolid, 47011 Spain)

  • Luis R. Izquierdo

    () (Social Systems Engineering Centre (InSiSoc), Valladolid, 47011 Spain
    Department of Civil Engineering, Universidad de Burgos, Burgos, 09001 Spain)

Abstract

The replicator-mutator dynamics is a set of differential equations frequently used in biological and socioeconomic contexts to model evolutionary processes subject to mutation, error or experimentation. The replicator-mutator dynamics generalizes the widely used replicator dynamics, which appears in this framework as the extreme case where replication is perfectly precise. This paper studies the influence of strictly dominated strategies on the location of the rest points of the replicator-mutator dynamics, at the limit where the mutation terms become arbitrarily small. It can be proved that such limit rest points for small mutation are Nash equilibria, so strictly dominated strategies do not occur at limit stationary points. However, we show through a simple case how strictly dominated strategies can have an influence on the location of the limit rest points for small mutation. Consequently, the characterization of the limit rest points of the replicator-mutator dynamics cannot in general proceed safely by readily eliminating strictly dominated strategies.

Suggested Citation

  • Segismundo S. Izquierdo & Luis R. Izquierdo, 2011. "Strictly Dominated Strategies in the Replicator-Mutator Dynamics," Games, MDPI, Open Access Journal, vol. 2(3), pages 1-10, September.
  • Handle: RePEc:gam:jgames:v:2:y:2011:i:3:p:355-364:d:13950
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    References listed on IDEAS

    as
    1. Samuelson, L., 1989. "Evolutionnary Stability In Asymmetric Games," Papers 11-8-2, Pennsylvania State - Department of Economics.
    2. Hofbauer, Josef & Weibull, Jorgen W., 1996. "Evolutionary Selection against Dominated Strategies," Journal of Economic Theory, Elsevier, vol. 71(2), pages 558-573, November.
    3. Hofbauer, Josef & Sandholm, William H., 2011. "Survival of dominated strategies under evolutionary dynamics," Theoretical Economics, Econometric Society, vol. 6(3), September.
    4. Ken Binmore & Larry Samuelson, 1999. "Evolutionary Drift and Equilibrium Selection," Review of Economic Studies, Oxford University Press, vol. 66(2), pages 363-393.
    5. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
    6. Vega-Redondo,Fernando, 2003. "Economics and the Theory of Games," Cambridge Books, Cambridge University Press, number 9780521775908, Fall.
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    Cited by:

    1. Situngkir, Hokky & Prasetyo, Yanu Endar, 2012. "On social and economic spheres: an observation of the “gantangan” Indonesian tradition," MPRA Paper 39671, University Library of Munich, Germany.

    More about this item

    Keywords

    replicator-mutator; dominated strategies; limit stationary states; limit rest points;

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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