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Selection-Mutation Dynamics of Signaling Games

Author

Listed:
  • Josef Hofbauer

    (Department of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, A-1090 Vienna, Austria)

  • Simon M. Huttegger

    (Department of Logic and Philosophy of Science, University of California at Irvine, 3151 Social Science Plaza A, Irvine, CA 92697, USA)

Abstract

We study the structure of the rest points of signaling games and their dynamic behavior under selection-mutation dynamics by taking the case of three signals as our canonical example. Many rest points of the replicator dynamics of signaling games are not isolated and, therefore, not robust under perturbations. However, some of them attract open sets of initial conditions. We prove the existence of certain rest points of the selection-mutation dynamics close to Nash equilibria of the signaling game and show that all but the perturbed rest points close to strict Nash equilibria are dynamically unstable. This is an important result for the evolution of signaling behavior, since it shows that the second-order forces that are governed by mutation can increase the chances of successful signaling.

Suggested Citation

  • Josef Hofbauer & Simon M. Huttegger, 2015. "Selection-Mutation Dynamics of Signaling Games," Games, MDPI, vol. 6(1), pages 1-30, January.
    • Handle: RePEc:gam:jgames:v:6:y:2015:i:1:p:2-31:d:44539
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    References listed on IDEAS

    as
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    5. Pawlowitsch, Christina, 2008. "Why evolution does not always lead to an optimal signaling system," Games and Economic Behavior, Elsevier, vol. 63(1), pages 203-226, May.
    6. Ritzberger, Klaus, 2002. "Foundations of Non-Cooperative Game Theory," OUP Catalogue, Oxford University Press, number 9780199247868.
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    Cited by:

    1. Seigo Uchida, 2019. "Efficiency and stability in sender-receiver games under the selection-mutation dynamics," Working Papers e132, Tokyo Center for Economic Research.
    2. Simon M. Huttegger & Kevin J. S. Zollman, 2016. "The Robustness of Hybrid Equilibria in Costly Signaling Games," Dynamic Games and Applications, Springer, vol. 6(3), pages 347-358, September.
    3. Seigo Uchida & Masakazu Fukuzumi, 2017. "The dynamical stability for an evolutionary language game under selection-mutation dynamics," Working Papers e115, Tokyo Center for Economic Research.

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