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Quantal response methods for equilibrium selection in 2×2 coordination games

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  • Zhang, Boyu
  • Hofbauer, Josef

Abstract

The notion of quantal response equilibrium (QRE), introduced by McKelvey and Palfrey (1995), has been widely used to explain experimental data. In this paper, we use quantal response equilibrium as a homotopy method for equilibrium selection, and study this in detail for 2×2 bimatrix coordination games. We show that the risk dominant equilibrium need not be selected. In the logarithmic game, the limiting QRE is the Nash equilibrium with the larger sum of square root payoffs. Finally, we apply the quantal response methods to the mini public goods game with punishment. A cooperative equilibrium can be selected if punishment is strong enough.

Suggested Citation

  • Zhang, Boyu & Hofbauer, Josef, 2016. "Quantal response methods for equilibrium selection in 2×2 coordination games," Games and Economic Behavior, Elsevier, vol. 97(C), pages 19-31.
    • Handle: RePEc:eee:gamebe:v:97:y:2016:i:c:p:19-31
    DOI: 10.1016/j.geb.2016.03.002
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    4. Qiang Wang & Linjie Liu & Xiaojie Chen, 2020. "Evolutionary Dynamics of Cooperation in the Public Goods Game with Individual Disguise and Peer Punishment," Dynamic Games and Applications, Springer, vol. 10(3), pages 764-782, September.
    5. 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.
    6. Rodrigo A. Velez & Alexander L. Brown, 2018. "Empirical Equilibrium," Papers 1804.07986, arXiv.org, revised Jul 2020.
    7. Emerson Melo, 2022. "On the uniqueness of quantal response equilibria and its application to network games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(3), pages 681-725, October.
    8. Zhang, Boyu, 2016. "Quantal response methods for equilibrium selection in normal form games," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 113-123.
    9. Ryoji Sawa, 2022. "Statistical Inference in Evolutionary Dynamics," Working Papers e170, Tokyo Center for Economic Research.
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    11. Cao, Yiyin & Dang, Chuangyin, 2022. "A variant of Harsanyi's tracing procedures to select a perfect equilibrium in normal form games," Games and Economic Behavior, Elsevier, vol. 134(C), pages 127-150.

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    More about this item

    Keywords

    Quantal response equilibrium; Equilibrium selection; Logit equilibrium; Logarithmic game; Punishment;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D58 - Microeconomics - - General Equilibrium and Disequilibrium - - - Computable and Other Applied General Equilibrium Models

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