IDEAS home Printed from https://ideas.repec.org/a/spr/etbull/v3y2015i1d10.1007_s40505-014-0062-4.html
   My bibliography  Save this article

Evolutionary dynamics and dominated strategies

Author

Listed:
  • Yannick Viossat

    (PSL, Université Paris-Dauphine, CEREMADE UMR 7534)

Abstract

Do evolutionary processes lead economic or biological agents to behave as if they were rational? To test this idea, many authors examined whether evolutionary game dynamics eliminate strictly dominated strategies. We survey, unify, and fill some gaps in this literature in the case of monotonic dynamics: a class of selection dynamics in which the growth rates of the pure strategies are ordered in accordance with their payoffs. We also survey results for other dynamics.

Suggested Citation

  • Yannick Viossat, 2015. "Evolutionary dynamics and dominated strategies," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 91-113, April.
  • Handle: RePEc:spr:etbull:v:3:y:2015:i:1:d:10.1007_s40505-014-0062-4
    DOI: 10.1007/s40505-014-0062-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s40505-014-0062-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s40505-014-0062-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Viossat, Yannick, 2007. "The replicator dynamics does not lead to correlated equilibria," Games and Economic Behavior, Elsevier, vol. 59(2), pages 397-407, May.
    2. Cabrales, Antonio & Sobel, Joel, 1992. "On the limit points of discrete selection dynamics," Journal of Economic Theory, Elsevier, vol. 57(2), pages 407-419, August.
    3. Hopkins, Ed, 1999. "Learning, Matching, and Aggregation," Games and Economic Behavior, Elsevier, vol. 26(1), pages 79-110, January.
    4. Sandholm, William H. & DokumacI, Emin & Lahkar, Ratul, 2008. "The projection dynamic and the replicator dynamic," Games and Economic Behavior, Elsevier, vol. 64(2), pages 666-683, November.
    5. Berger, Ulrich & Hofbauer, Josef, 2006. "Irrational behavior in the Brown-von Neumann-Nash dynamics," Games and Economic Behavior, Elsevier, vol. 56(1), pages 1-6, July.
    6. Armen A. Alchian, 1950. "Uncertainty, Evolution, and Economic Theory," Journal of Political Economy, University of Chicago Press, vol. 58, pages 211-211.
    7. Gaunersdorfer Andrea & Hofbauer Josef, 1995. "Fictitious Play, Shapley Polygons, and the Replicator Equation," Games and Economic Behavior, Elsevier, vol. 11(2), pages 279-303, November.
    8. Viossat, Yannick, 2008. "Evolutionary dynamics may eliminate all strategies used in correlated equilibrium," Mathematical Social Sciences, Elsevier, vol. 56(1), pages 27-43, July.
    9. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    10. Elyès Jouini & Clotilde Napp & Yannick Viossat, 2013. "Evolutionary Beliefs and Financial Markets," Review of Finance, European Finance Association, vol. 17(2), pages 727-766.
    11. Dekel, Eddie & Scotchmer, Suzanne, 1992. "On the evolution of optimizing behavior," Journal of Economic Theory, Elsevier, vol. 57(2), pages 392-406, August.
    12. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
    13. Fudenberg, D. & Harris, C., 1992. "Evolutionary dynamics with aggregate shocks," Journal of Economic Theory, Elsevier, vol. 57(2), pages 420-441, August.
    14. Balkenborg, Dieter & Hofbauer, Josef & Kuzmics, Christoph, 2016. "Refined best reply correspondence and dynamics," Center for Mathematical Economics Working Papers 451, Center for Mathematical Economics, Bielefeld University.
    15. Cressman, Ross, 2005. "Stability of the replicator equation with continuous strategy space," Mathematical Social Sciences, Elsevier, vol. 50(2), pages 127-147, September.
    16. Josef Hofbauer & Karl H. Schlag, 2000. "Sophisticated imitation in cyclic games," Journal of Evolutionary Economics, Springer, vol. 10(5), pages 523-543.
    17. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-867, May.
    18. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    19. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-666, May.
    20. repec:dau:papers:123456789/5772 is not listed on IDEAS
    21. Josef Hofbauer & Sylvain Sorin & Yannick Viossat, 2009. "Time Average Replicator and Best-Reply Dynamics," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 263-269, May.
    22. Laraki, Rida & Mertikopoulos, Panayotis, 2013. "Higher order game dynamics," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2666-2695.
    23. Michael J. Smith, 1984. "The Stability of a Dynamic Model of Traffic Assignment---An Application of a Method of Lyapunov," Transportation Science, INFORMS, vol. 18(3), pages 245-252, August.
    24. repec:dau:papers:123456789/1061 is not listed on IDEAS
    25. repec:dau:papers:123456789/1119 is not listed on IDEAS
    26. Weibull, Jorgen W., 1994. "The 'as if' approach to game theory: Three positive results and four obstacles," European Economic Review, Elsevier, vol. 38(3-4), pages 868-881, April.
    27. Cabrales, Antonio, 2000. "Stochastic Replicator Dynamics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(2), pages 451-481, May.
    28. Nachbar, J H, 1990. ""Evolutionary" Selection Dynamics in Games: Convergence and Limit Properties," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(1), pages 59-89.
    29. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
    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. Bernergård, Axel & Mohlin, Erik, 2019. "Evolutionary selection against iteratively weakly dominated strategies," Games and Economic Behavior, Elsevier, vol. 117(C), pages 82-97.
    2. George Loginov, 2019. "Ordinal Imitative Dynamics," Papers 1907.04272, arXiv.org.

    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. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. Abhijit Banerjee & Jörgen W. Weibull & Ken Binmore, 1996. "Evolution and Rationality: Some Recent Game-Theoretic Results," International Economic Association Series, in: Beth Allen (ed.), Economics in a Changing World, chapter 4, pages 90-117, Palgrave Macmillan.
    3. Viossat, Yannick, 2008. "Evolutionary dynamics may eliminate all strategies used in correlated equilibrium," Mathematical Social Sciences, Elsevier, vol. 56(1), pages 27-43, July.
    4. Weibull, Jörgen W., 1992. "An Introduction to Evolutionary Game Theory," Working Paper Series 347, Research Institute of Industrial Economics.
    5. Weibull, Jörgen W., 1997. "What have we learned from Evolutionary Game Theory so far?," Working Paper Series 487, Research Institute of Industrial Economics, revised 26 Oct 1998.
    6. Jonathan Bendor & Piotr Swistak, 1998. "Evolutionary Equilibria: Characterization Theorems and Their Implications," Theory and Decision, Springer, vol. 45(2), pages 99-159, October.
    7. Christoph Kuzmics & Daniel Rodenburger, 2020. "A case of evolutionarily stable attainable equilibrium in the laboratory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 685-721, October.
    8. Yannick Viossat, 2011. "Deterministic monotone dynamics and dominated strategies," Working Papers hal-00636620, HAL.
    9. Panayotis Mertikopoulos & William H. Sandholm, 2016. "Learning in Games via Reinforcement and Regularization," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1297-1324, November.
    10. Sandholm,W.H., 2003. "Excess payoff dynamics, potential dynamics, and stable games," Working papers 5, Wisconsin Madison - Social Systems.
    11. Berger, Ulrich & Hofbauer, Josef, 2006. "Irrational behavior in the Brown-von Neumann-Nash dynamics," Games and Economic Behavior, Elsevier, vol. 56(1), pages 1-6, July.
    12. Yannick Viossat, 2012. "Game Dynamics and Nash Equilibria," Working Papers hal-00756096, HAL.
    13. Laraki, Rida & Mertikopoulos, Panayotis, 2013. "Higher order game dynamics," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2666-2695.
    14. Fabrizio Germano, 2007. "Stochastic Evolution of Rules for Playing Finite Normal Form Games," Theory and Decision, Springer, vol. 62(4), pages 311-333, May.
    15. Marimon, R. & McGraltan, E., 1993. "On Adaptative Learning in Strategic Games," Papers 190, Cambridge - Risk, Information & Quantity Signals.
    16. Sandholm, William H., 2001. "Potential Games with Continuous Player Sets," Journal of Economic Theory, Elsevier, vol. 97(1), pages 81-108, March.
    17. Panayotis Mertikopoulos & Yannick Viossat, 2016. "Imitation dynamics with payoff shocks," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 291-320, March.
    18. Dawid, Herbert, 1999. "On the stability of monotone discrete selection dynamics with inertia," Mathematical Social Sciences, Elsevier, vol. 37(3), pages 265-280, May.
    19. Reinoud Joosten, 2009. "Paul Samuelson's critique and equilibrium concepts in evolutionary game theory," Papers on Economics and Evolution 2009-16, Philipps University Marburg, Department of Geography.
    20. William H. Sandholm, 1997. "An Evolutionary Approach to Congestion," Discussion Papers 1198, Northwestern University, Center for Mathematical Studies in Economics and Management Science.

    More about this item

    Keywords

    As-if rationality; Evolutionary games; Dominated strategies; Replicator dynamics; Monotonic dynamics; Innovative dynamics;
    All these keywords.

    JEL classification:

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

    Statistics

    Access and download statistics

    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:spr:etbull:v:3:y:2015:i:1:d:10.1007_s40505-014-0062-4. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: http://www.springer.com .

    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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.