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Survival of dominated strategies under evolutionary dynamics

Author

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  • ,

    (Department of Mathematics, University of Vienna)

  • , H.

    (Department of Economics, University of Wisconsin)

Abstract

We prove that any deterministic evolutionary dynamic satisfying four mild requirements fails to eliminate strictly dominated strategies in some games. We also show that existing elimination results for evolutionary dynamics are not robust to small changes in the specifications of the dynamics. Numerical analysis reveals that dominated strategies can persist at nontrivial frequencies even when the level of domination is not small.

Suggested Citation

  • , & , H., 2011. "Survival of dominated strategies under evolutionary dynamics," Theoretical Economics, Econometric Society, vol. 6(3), September.
    • Handle: RePEc:the:publsh:771
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    Blog mentions

    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. “Survival of Dominated Strategies Under Evolutionary Dynamics,” J. Hofbauer & W. Sandholm (2011)
      by afinetheorem in A Fine Theorem on 2012-09-06 11:00:48
    2. “Survival of Dominated Strategies Under Evolutionary Dynamics,” J. Hofbauer & W. Sandholm (2011)
      by afinetheorem in A Fine Theorem on 2012-09-06 11:00:48

    Citations

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    Cited by:

    1. Jonas Hedlund & Carlos Oyarzun, 2018. "Imitation in heterogeneous populations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(4), pages 937-973, June.
    2. 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.
    3. Sawa, Ryoji & Zusai, Dai, 2019. "Evolutionary dynamics in multitasking environments," Journal of Economic Behavior & Organization, Elsevier, vol. 166(C), pages 288-308.
    4. Yannick Viossat, 2012. "Game Dynamics and Nash Equilibria," Working Papers hal-00756096, HAL.
    5. 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.
    6. , & , H. & ,, 2015. "Sampling best response dynamics and deterministic equilibrium selection," Theoretical Economics, Econometric Society, vol. 10(1), January.
    7. Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2012. "Perturbations of Set-Valued Dynamical Systems, with Applications to Game Theory," Dynamic Games and Applications, Springer, vol. 2(2), pages 195-205, June.
    8. Laraki, Rida & Mertikopoulos, Panayotis, 2013. "Higher order game dynamics," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2666-2695.
    9. Sandholm, William H. & Izquierdo, Segismundo S. & Izquierdo, Luis R., 2020. "Stability for best experienced payoff dynamics," Journal of Economic Theory, Elsevier, vol. 185(C).
    10. 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.
    11. Itai Arieli & H Peyton Young, 2011. "Stochastic Learning Dynamics and Speed of Convergence in Population Games," Economics Series Working Papers 570, University of Oxford, Department of Economics.
    12. Zhang, Boyu, 2016. "Quantal response methods for equilibrium selection in normal form games," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 113-123.
    13. Pandey, Ayush & Lehe, Lewis J., 2024. "Congestive mode-switching and economies of scale on a bus route," Transportation Research Part B: Methodological, Elsevier, vol. 183(C).
    14. George Loginov, 2022. "Ordinal imitative dynamics," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(2), pages 391-412, June.
    15. Wolfgang Kuhle, 2016. "An Equilibrium Model with Computationally Constrained Agents," Papers 1611.01771, arXiv.org.
    16. Segismundo S. Izquierdo & Luis R. Izquierdo, 2011. "Strictly Dominated Strategies in the Replicator-Mutator Dynamics," Games, MDPI, vol. 2(3), pages 1-10, September.
    17. Bernergård, Axel & Mohlin, Erik, 2019. "Evolutionary selection against iteratively weakly dominated strategies," Games and Economic Behavior, Elsevier, vol. 117(C), pages 82-97.
    18. Wang Yijia & Wang Zhijian, 2023. "Pulse in collapse: a game dynamics experiment," Papers 2302.09336, arXiv.org.
    19. Jakub Bielawski & {L}ukasz Cholewa & Fryderyk Falniowski, 2024. "The emergence of chaos in population game dynamics induced by comparisons," Papers 2412.06037, arXiv.org.

    More about this item

    Keywords

    Evolutionary game theory; evolutionary game dynamics; nonconvergnece; dominated strategies;
    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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