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Evolutionary selection against iteratively weakly dominated strategies

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  • Bernergård, Axel
  • Mohlin, Erik

Abstract

This paper provides sufficient conditions under which regular payoff monotonic evolutionary dynamics (a class of imitative dynamics that includes the replicator dynamic) select against strategies that do not survive a sequence of iterated elimination of weakly dominated strategies. We apply these conditions to Bertrand duopolies and first-price auctions. Our conditions also imply evolutionary selection against iteratively strictly dominated strategies.

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  • Bernergård, Axel & Mohlin, Erik, 2019. "Evolutionary selection against iteratively weakly dominated strategies," Games and Economic Behavior, Elsevier, vol. 117(C), pages 82-97.
    • Handle: RePEc:eee:gamebe:v:117:y:2019:i:c:p:82-97
    DOI: 10.1016/j.geb.2019.05.009
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    as
    1. Ponti, Giovanni, 2000. "Cycles of Learning in the Centipede Game," Games and Economic Behavior, Elsevier, vol. 30(1), pages 115-141, January.
    2. Erev, Ido & Roth, Alvin E, 1998. "Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria," American Economic Review, American Economic Association, vol. 88(4), pages 848-881, September.
    3. Arthur, W Brian, 1993. "On Designing Economic Agents That Behave Like Human Agents," Journal of Evolutionary Economics, Springer, vol. 3(1), pages 1-22, February.
    4. 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.
    5. Hofbauer, Josef & Weibull, Jorgen W., 1996. "Evolutionary Selection against Dominated Strategies," Journal of Economic Theory, Elsevier, vol. 71(2), pages 558-573, November.
    6. Matthew Embrey & Guillaume R Fréchette & Sevgi Yuksel, 2018. "Cooperation in the Finitely Repeated Prisoner’s Dilemma," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(1), pages 509-551.
    7. Mohlin, Erik, 2012. "Evolution of theories of mind," Games and Economic Behavior, Elsevier, vol. 75(1), pages 299-318.
    8. Marx, Leslie M. & Swinkels, Jeroen M., 2000. "Order Independence for Iterated Weak Dominance," Games and Economic Behavior, Elsevier, vol. 31(2), pages 324-329, May.
    9. , & , H., 2011. "Survival of dominated strategies under evolutionary dynamics," Theoretical Economics, Econometric Society, vol. 6(3), September.
    10. Tan, Tommy Chin-Chiu & da Costa Werlang, Sergio Ribeiro, 1988. "The Bayesian foundations of solution concepts of games," Journal of Economic Theory, Elsevier, vol. 45(2), pages 370-391, August.
    11. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    12. Ed Hopkins, 2002. "Two Competing Models of How People Learn in Games," Econometrica, Econometric Society, vol. 70(6), pages 2141-2166, November.
    13. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
    14. Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033054, April.
    15. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    16. Asheim, Geir B. & Dufwenberg, Martin, 2003. "Admissibility and common belief," Games and Economic Behavior, Elsevier, vol. 42(2), pages 208-234, February.
    17. Nax, Heinrich H. & Burton-Chellew, Maxwell N. & West, Stuart A. & Young, H. Peyton, 2016. "Learning in a black box," LSE Research Online Documents on Economics 68714, London School of Economics and Political Science, LSE Library.
    18. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
    19. Nax, Heinrich H. & Burton-Chellew, Maxwell N. & West, Stuart A. & Young, H. Peyton, 2016. "Learning in a black box," Journal of Economic Behavior & Organization, Elsevier, vol. 127(C), pages 1-15.
    20. Adam Brandenburger & Amanda Friedenberg & H. Jerome Keisler, 2014. "Admissibility in Games," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 7, pages 161-212, World Scientific Publishing Co. Pte. Ltd..
    21. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-1326, December.
    22. Kuzmics, Christoph, 2011. "On the elimination of dominated strategies in stochastic models of evolution with large populations," Games and Economic Behavior, Elsevier, vol. 72(2), pages 452-466, June.
    23. Milgrom, Paul & Roberts, John, 1991. "Adaptive and sophisticated learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 82-100, February.
    24. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    25. Cressman, R., 1996. "Evolutionary Stability in the Finitely Repeated Prisoner 's Dilemma Game," Journal of Economic Theory, Elsevier, vol. 68(1), pages 234-248, January.
    26. Marx, Leslie M., 1999. "Adaptive Learning and Iterated Weak Dominance," Games and Economic Behavior, Elsevier, vol. 26(2), pages 253-278, January.
    27. repec:dau:papers:123456789/14432 is not listed on IDEAS
    28. Laraki, Rida & Mertikopoulos, Panayotis, 2013. "Higher order game dynamics," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2666-2695.
    29. John G. Cross, 1973. "A Stochastic Learning Model of Economic Behavior," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 87(2), pages 239-266.
    30. 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.
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    Cited by:

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    3. Heller, Yuval & Kuzmics, Christoph, 2024. "Communication, renegotiation and coordination with private values," Games and Economic Behavior, Elsevier, vol. 143(C), pages 51-76.
    4. 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.
    5. Ellingsen, Tore & Mohlin, Erik, 2019. "Decency," Working Papers 2019:3, Lund University, Department of Economics.

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    More about this item

    Keywords

    Iterated elimination of weakly dominated strategies; Iterated admissibility; Payoff monotonicity; Convex monotonicity; Evolutionary dynamics; Replicator dynamic;
    All these keywords.

    JEL classification:

    • 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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