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Endogenous quantal response equilibrium

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  • Friedman, Evan

Abstract

We endogenize the precision parameter λ of logit quantal response equilibrium (LQRE). In the first stage of an endogenous quantal response equilibrium (EQRE), each player chooses her precision optimally subject to costs, taking as given other players’ (second-stage) behavior. In the second stage, the distribution of players’ actions is a heterogenous LQRE given the profile of first-stage precision choices. EQRE satisfies a modified version of the regularity axioms, nests LQRE as a limiting case for a sequence of cost functions, and admits analogues of classic results for LQRE such as those for equilibrium selection. We show how EQRE differs from LQRE using the family of generalized matching pennies games.

Suggested Citation

  • Friedman, Evan, 2020. "Endogenous quantal response equilibrium," Games and Economic Behavior, Elsevier, vol. 124(C), pages 620-643.
    • Handle: RePEc:eee:gamebe:v:124:y:2020:i:c:p:620-643
    DOI: 10.1016/j.geb.2020.10.003
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    1. Wolpert David & Jamison Julian & Newth David & Harre Michael, 2011. "Strategic Choice of Preferences: the Persona Model," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-39, August.
    2. McKelvey, Richard D. & Palfrey, Thomas R. & Weber, Roberto A., 2000. "The effects of payoff magnitude and heterogeneity on behavior in 2 x 2 games with unique mixed strategy equilibria," Journal of Economic Behavior & Organization, Elsevier, vol. 42(4), pages 523-548, August.
    3. Rogers, Brian W. & Palfrey, Thomas R. & Camerer, Colin F., 2009. "Heterogeneous quantal response equilibrium and cognitive hierarchies," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1440-1467, July.
    4. Richard Mckelvey & Thomas Palfrey, 1998. "Quantal Response Equilibria for Extensive Form Games," Experimental Economics, Springer;Economic Science Association, vol. 1(1), pages 9-41, June.
    5. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
    6. Stahl, D O, 1990. "Entropy Control Costs and Entropic Equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(2), pages 129-138.
    7. Jacob Goeree & Charles Holt & Thomas Palfrey, 2005. "Regular Quantal Response Equilibrium," Experimental Economics, Springer;Economic Science Association, vol. 8(4), pages 347-367, December.
    8. Mattsson, Lars-Goran & Weibull, Jorgen W., 2002. "Probabilistic choice and procedurally bounded rationality," Games and Economic Behavior, Elsevier, vol. 41(1), pages 61-78, October.
    9. Jörgen Weibull & Lars-Göran Mattsson & Mark Voorneveld, 2007. "Better May be Worse: Some Monotonicity Results and Paradoxes in Discrete Choice Under Uncertainty," Theory and Decision, Springer, vol. 63(2), pages 121-151, September.
    10. Jacob K. Goeree & Charles A. Holt & Thomas R. Palfrey, 2016. "Quantal Response Equilibrium:A Stochastic Theory of Games," Economics Books, Princeton University Press, edition 1, number 10743.
    11. Daniel L. McFadden, 1976. "Quantal Choice Analysis: A Survey," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 363-390, National Bureau of Economic Research, Inc.
    12. Yang, Ming, 2015. "Coordination with flexible information acquisition," Journal of Economic Theory, Elsevier, vol. 158(PB), pages 721-738.
    13. Richard D. Mckelvey & Thomas R. Palfrey, 1996. "A Statistical Theory Of Equilibrium In Games," The Japanese Economic Review, Japanese Economic Association, vol. 47(2), pages 186-209, June.
    14. Colin F. Camerer & Teck-Hua Ho & Juin-Kuan Chong, 2004. "A Cognitive Hierarchy Model of Games," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(3), pages 861-898.
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    Cited by:

    1. Nunnari, Salvatore & Frydman, Cary, 2021. "Coordination with Cognitive Noise," CEPR Discussion Papers 16644, C.E.P.R. Discussion Papers.
    2. Matthew Kovach & Gerelt Tserenjigmid, 2023. "The Focal Quantal Response Equilibrium," Papers 2304.00438, arXiv.org.
    3. Benjamin Patrick Evans & Mikhail Prokopenko, 2021. "Bounded rationality for relaxing best response and mutual consistency: The Quantal Hierarchy model of decision-making," Papers 2106.15844, arXiv.org, revised Mar 2023.
    4. Benjamin Patrick Evans & Mikhail Prokopenko, 2024. "Bounded rationality for relaxing best response and mutual consistency: the quantal hierarchy model of decision making," Theory and Decision, Springer, vol. 96(1), pages 71-111, February.
    5. 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.
    6. Guy Aridor & Rava Azeredo da Silveira & Michael Woodford, 2024. "Information-Constrained Coordination of Economic Behavior," CESifo Working Paper Series 10935, CESifo.

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    More about this item

    Keywords

    Quantal response equilibrium; Logit; Endogenous; Discrete choice models;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C92 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Group Behavior

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