IDEAS home Printed from https://ideas.repec.org/a/gam/jgames/v6y2015i1p2-31d44539.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2073-4336/6/1/2/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2073-4336/6/1/2/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ritzberger, Klaus, 2002. "Foundations of Non-Cooperative Game Theory," OUP Catalogue, Oxford University Press, number 9780199247868.
    2. repec:cup:cbooks:9780521555838 is not listed on IDEAS
    3. Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033054, December.
    4. Ken Binmore & Larry Samuelson, 1999. "Evolutionary Drift and Equilibrium Selection," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(2), pages 363-393.
    5. Jansen M. J. M. & Jurg A. P. & Borm P. E. M., 1994. "On Strictly Perfect Sets," Games and Economic Behavior, Elsevier, vol. 6(3), pages 400-415, May.
    6. Ken Binmore & Larry Samuelson, "undated". "Evolutionary Drift And Equilibrium Selection," ELSE working papers 049, ESRC Centre on Economics Learning and Social Evolution.
    7. 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.
    8. Ken Binmore & Larry Samuelson, "undated". "Evolutionary Drift and Equilibrium Selection," ELSE working papers 011, ESRC Centre on Economics Learning and Social Evolution.
    9. Crawford, Vincent P & Sobel, Joel, 1982. "Strategic Information Transmission," Econometrica, Econometric Society, vol. 50(6), pages 1431-1451, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. K.J.M. De Jaegher & R. van Rooij, 2011. "Game-theoretic pragmatics under conflicting and common interests," Working Papers 11-25, Utrecht School of Economics.
    2. Poulsen, Anders Udo, 2007. "Information and endogenous first mover advantages in the ultimatum game: An evolutionary approach," Journal of Economic Behavior & Organization, Elsevier, vol. 64(1), pages 129-143, September.
    3. Russell Golman & Scott Page, 2010. "Basins of attraction and equilibrium selection under different learning rules," Journal of Evolutionary Economics, Springer, vol. 20(1), pages 49-72, January.
    4. Lindgren, Kristian & Verendel, Vilhelm, 2013. "Evolutionary Exploration of the Finitely Repeated Prisoners' Dilemma--The Effect of Out-of-Equilibrium Play," MPRA Paper 43662, University Library of Munich, Germany.
    5. Kristian Lindgren & Vilhelm Verendel, 2013. "Evolutionary Exploration of the Finitely Repeated Prisoners’ Dilemma—The Effect of Out-of-Equilibrium Play," Games, MDPI, vol. 4(1), pages 1-20, January.
    6. Heller, Yuval & Kuzmics, Christoph, 2020. "Communication, Renegotiation and Coordination with Private Values (Extended Version)," MPRA Paper 102926, University Library of Munich, Germany, revised 26 Jul 2021.
    7. Ianni, A., 2002. "Reinforcement learning and the power law of practice: some analytical results," Discussion Paper Series In Economics And Econometrics 203, Economics Division, School of Social Sciences, University of Southampton.
    8. William Tracy, 2014. "Paradox Lost: The Evolution of Strategies in Selten’s Chain Store Game," Computational Economics, Springer;Society for Computational Economics, vol. 43(1), pages 83-103, January.
    9. Waters, George A., 2009. "Chaos in the cobweb model with a new learning dynamic," Journal of Economic Dynamics and Control, Elsevier, vol. 33(6), pages 1201-1216, June.
    10. Sandholm,W.H., 2003. "Excess payoff dynamics, potential dynamics, and stable games," Working papers 5, Wisconsin Madison - Social Systems.
    11. Weibull, Jörgen & Salomonsson, Marcus, 2005. "Natural selection and social preferences," SSE/EFI Working Paper Series in Economics and Finance 588, Stockholm School of Economics, revised 27 Sep 2005.
    12. Antonio Cabrales & Giovanni Ponti, 2000. "Implementation, Elimination of Weakly Dominated Strategies and Evolutionary Dynamics," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(2), pages 247-282, April.
    13. Agastya, Murali, 2004. "Stochastic stability in a double auction," Games and Economic Behavior, Elsevier, vol. 48(2), pages 203-222, August.
    14. Hauk, Esther & Hurkens, Sjaak, 2002. "On Forward Induction and Evolutionary and Strategic Stability," Journal of Economic Theory, Elsevier, vol. 106(1), pages 66-90, September.
    15. Yasuhiro Shirata, 2020. "Evolution of a Collusive Price in a Networked Market," Dynamic Games and Applications, Springer, vol. 10(2), pages 528-554, June.
    16. van Damme, Eric & Binmore, Kenneth G. & Roth, Alvin E. & Samuelson, Larry & Winter, Eyal & Bolton, Gary E. & Ockenfels, Axel & Dufwenberg, Martin & Kirchsteiger, Georg & Gneezy, Uri & Kocher, Martin G, 2014. "How Werner Güth's ultimatum game shaped our understanding of social behavior," Journal of Economic Behavior & Organization, Elsevier, vol. 108(C), pages 292-318.
    17. Ed Hopkins, 2002. "Two Competing Models of How People Learn in Games," Econometrica, Econometric Society, vol. 70(6), pages 2141-2166, November.
    18. Mathias Staudigl, 2010. "On a General class of stochastic co-evolutionary dynamics," Vienna Economics Papers 1001, University of Vienna, Department of Economics.
    19. Ponti, Giovanni, 2000. "Continuous-time evolutionary dynamics: theory and practice," Research in Economics, Elsevier, vol. 54(2), pages 187-214, June.
    20. Simon P. Anderson & Jacob K. Goeree & Charles A. Holt, 2002. "The Logit Equilibrium: A Perspective on Intuitive Behavioral Anomalies," Southern Economic Journal, John Wiley & Sons, vol. 69(1), pages 21-47, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jgames:v:6:y:2015:i:1:p:2-31:d:44539. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.