IDEAS home Printed from https://ideas.repec.org/p/hhs/lunewp/2017_018.html
   My bibliography  Save this paper

Evolutionary Selection against Iteratively Weakly Dominated Strategies

Author

Listed:
  • Bernergård, Axel

    (Department of Economics, Södertörn University)

  • Mohlin, Erik

    (Department of Economics, Lund University)

Abstract

This paper provides sufficient conditions under which convex monotonic evolutionary dynamics (a class of imitative dynamics that includes the replicator dynamic) select against strategies that do not survive iterated elimination of weakly dominated strategies. We apply these conditions to Bertrand duopolies, first-price auctions, finitely repeated Prisoner's Dilemmas, and the p-Beauty Contests. Our conditions also imply evolutionary selection against all iteratively strictly dominated strategies.

Suggested Citation

  • Bernergård, Axel & Mohlin, Erik, 2017. "Evolutionary Selection against Iteratively Weakly Dominated Strategies," Working Papers 2017:18, Lund University, Department of Economics, revised 12 Nov 2018.
    • Handle: RePEc:hhs:lunewp:2017_018
    as

    Download full text from publisher

    File URL: http://project.nek.lu.se/publications/workpap/papers/wp17_18.pdf
    File Function: Full text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    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. 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.
    3. Hofbauer, Josef & Weibull, Jorgen W., 1996. "Evolutionary Selection against Dominated Strategies," Journal of Economic Theory, Elsevier, vol. 71(2), pages 558-573, November.
    4. , & , H., 2011. "Survival of dominated strategies under evolutionary dynamics," Theoretical Economics, Econometric Society, vol. 6(3), September.
    5. 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.
    6. 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.
    7. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
    8. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    9. Asheim, Geir B. & Dufwenberg, Martin, 2003. "Admissibility and common belief," Games and Economic Behavior, Elsevier, vol. 42(2), pages 208-234, February.
    10. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
    11. 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.
    12. 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..
    13. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-1326, December.
    14. 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.
    15. Ed Hopkins, 2002. "Two Competing Models of How People Learn in Games," Econometrica, Econometric Society, vol. 70(6), pages 2141-2166, November.
    16. 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.
    17. repec:dau:papers:123456789/14432 is not listed on IDEAS
    18. Laraki, Rida & Mertikopoulos, Panayotis, 2013. "Higher order game dynamics," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2666-2695.
    19. Mohlin, Erik, 2012. "Evolution of theories of mind," Games and Economic Behavior, Elsevier, vol. 75(1), pages 299-318.
    20. 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.
    21. 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.
    22. 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.
    23. 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.
    24. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    25. Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033054, April.
    26. 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.
    27. 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.
    28. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    29. Marx, Leslie M., 1999. "Adaptive Learning and Iterated Weak Dominance," Games and Economic Behavior, Elsevier, vol. 26(2), pages 253-278, January.
    30. 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.
    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. Heller, Yuval & Kuzmics, Christoph, 2024. "Communication, renegotiation and coordination with private values," Games and Economic Behavior, Elsevier, vol. 143(C), pages 51-76.
    2. Yuval Heller & Christoph Kuzmics, 2019. "Renegotiation and Coordination with Private Values," Graz Economics Papers 2019-10, University of Graz, Department of Economics.
    3. 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.
    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.

    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. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    2. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    3. 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.
    4. Mohlin, Erik & Östling, Robert & Wang, Joseph Tao-yi, 2020. "Learning by similarity-weighted imitation in winner-takes-all games," Games and Economic Behavior, Elsevier, vol. 120(C), pages 225-245.
    5. Ponti, Giovanni, 2000. "Continuous-time evolutionary dynamics: theory and practice," Research in Economics, Elsevier, vol. 54(2), pages 187-214, June.
    6. 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.
    7. Mario Gilli, 2002. "Iterated Admissibility as Solution Concept in Game Theory," Working Papers 47, University of Milano-Bicocca, Department of Economics, revised Mar 2002.
    8. 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.
    9. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    10. Pangallo, Marco & Sanders, James B.T. & Galla, Tobias & Farmer, J. Doyne, 2022. "Towards a taxonomy of learning dynamics in 2 × 2 games," Games and Economic Behavior, Elsevier, vol. 132(C), pages 1-21.
    11. 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.
    12. Ponti, Giovanni, 2000. "Cycles of Learning in the Centipede Game," Games and Economic Behavior, Elsevier, vol. 30(1), pages 115-141, January.
    13. 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.
    14. Amanda Friedenberg & H. Jerome Keisler, 2021. "Iterated dominance revisited," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(2), pages 377-421, September.
    15. 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.
    16. Xiao Luo & Xuewen Qian & Chen Qu, 2020. "Iterated elimination procedures," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(2), pages 437-465, September.
    17. 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.
    18. Weibull, Jorgen W., 1998. "Evolution, rationality and equilibrium in games," European Economic Review, Elsevier, vol. 42(3-5), pages 641-649, May.
    19. Innocenti, Stefania & Cowan, Robin, 2019. "Self-efficacy beliefs and imitation: A two-armed bandit experiment," European Economic Review, Elsevier, vol. 113(C), pages 156-172.
    20. Burkhard C. Schipper & Hang Zhou, 2022. "Level-k Thinking in the Extensive Form," Working Papers 352, University of California, Davis, Department of Economics.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:hhs:lunewp:2017_018. 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: Iker Arregui Alegria (email available below). General contact details of provider: https://edirc.repec.org/data/delunse.html .

    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.