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Long-run equilibria with dominated strategies

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  • Kim, Chongmin
  • Wong, Kam-Chau

Abstract

We show that the predictions of long-run behavior under the evolutionary process are highly sensitive to the addition and elimination of strictly dominated strategies. In particular, for the best response dynamics [cf. Kandori, M., Rob, R., 1995. Evolution of equilibria in the long run: A general theory and applications. J. Econ. Theory 65 (2), 383-414] we prove that for any symmetric normal form game, any strict Nash equilibrium can be selected as the unique long-run equilibrium by appropriately adding only one single strategy which is strictly dominated by all original strategies. Moreover, if we further assume instantaneous adjustment, then any convex combination of strict Nash equilibria with rational number weights can be realized as the long-run distribution by appropriately adding strictly dominated strategies.

Suggested Citation

  • Kim, Chongmin & Wong, Kam-Chau, 2010. "Long-run equilibria with dominated strategies," Games and Economic Behavior, Elsevier, vol. 68(1), pages 242-254, January.
    • Handle: RePEc:eee:gamebe:v:68:y:2010:i:1:p:242-254
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    References listed on IDEAS

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    2. Weidenholzer, Simon, 2012. "Long-run equilibria, dominated strategies, and local interactions," Games and Economic Behavior, Elsevier, vol. 75(2), pages 1014-1024.
    3. Dietrichson, Jens & Gudmundsson, Jens & Jochem, Torsten, 2022. "Why don’t we talk about it? Communication and coordination in teams," Journal of Economic Behavior & Organization, Elsevier, vol. 197(C), pages 257-278.
    4. Jean-Paul Carvalho, 2017. "Coordination and culture," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(3), pages 449-475, October.
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    6. Weidenholzer, Simon, 2012. "Long-run equilibria, dominated strategies, and local interactions," Games and Economic Behavior, Elsevier, vol. 75(2), pages 1014-1024.
    7. Sawa, Ryoji, 2021. "A stochastic stability analysis with observation errors in normal form games," Games and Economic Behavior, Elsevier, vol. 129(C), pages 570-589.
    8. Simon Weidenholzer, 2010. "Coordination Games and Local Interactions: A Survey of the Game Theoretic Literature," Games, MDPI, vol. 1(4), pages 1-35, November.
    9. Zhang, Boyu, 2016. "Quantal response methods for equilibrium selection in normal form games," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 113-123.
    10. Jiang, Ge & Weidenholzer, Simon, 2014. "Local Interactions and Switching Costs," Economics Discussion Papers 9015, University of Essex, Department of Economics.
    11. Jiang, Ge & Weidenholzer, Simon, 2016. "Local Interactions under Switching Costs," Economics Discussion Papers 17770, University of Essex, Department of Economics.

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