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Survival of dominated strategies under evolutionary dynamics

Author

Listed:
  • Hofbauer, Josef

    () (Department of Mathematics, University of Vienna)

  • Sandholm, William 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

  • Hofbauer, Josef & Sandholm, William 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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    File URL: http://econtheory.org/ojs/index.php/te/article/viewFile/20110341/5735/192
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    Citations

    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. Bernergård, Axel & Mohlin, Erik, 2017. "Evolutionary Selection against Iteratively Weakly Dominated Strategies," Working Papers 2017:18, Lund University, Department of Economics.
    2. Hedlund, Jonas & Oyarzun, Carlos, 2016. "Imitation in Heterogeneous Populations," Working Papers 0625, University of Heidelberg, Department of Economics.
    3. 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.
    4. 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.
    5. Zhang, Boyu, 2016. "Quantal response methods for equilibrium selection in normal form games," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 113-123.
    6. Laraki, Rida & Mertikopoulos, Panayotis, 2013. "Higher order game dynamics," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2666-2695.
    7. Wolfgang Kuhle, 2016. "An Equilibrium Model with Computationally Constrained Agents," Papers 1611.01771, arXiv.org.
    8. Yannick Viossat, 2012. "Game Dynamics and Nash Equilibria," Working Papers hal-00756096, HAL.
    9. repec:spr:joecth:v:65:y:2018:i:4:d:10.1007_s00199-017-1044-1 is not listed on IDEAS
    10. Segismundo S. Izquierdo & Luis R. Izquierdo, 2011. "Strictly Dominated Strategies in the Replicator-Mutator Dynamics," Games, MDPI, Open Access Journal, vol. 2(3), pages 1-10, September.

    More about this item

    Keywords

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

    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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