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Regular quantal response equilibrium

Author

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  • Goeree, Jacob K.
  • Holt, Charles A.
  • Palfrey, Thomas R.

Abstract

The structural Quantal Response Equilibrium (QRE) generalizes the Nash equilibrium by augmenting payoffs with random elements that are not removed in some limit. This approach has been widely used both as a theoretical framework to study comparative statics of games and as an econometric framework to analyze experimental and field data. The framework of structural QRE is flexible: it can be applied to arbitrary finite games and incorporate very general error structures. Restrictions on the error structure are needed, however, to place testable restrictions on the data (Haile et al., 2004). This paper proposes a reduced-form approach, based on quantal response functions that replace the best-response functions underlying the Nash equilibrium. We define a {\em regular} QRE as a fixed point of quantal response functions that satisfies four axioms: continuity, interiority, responsiveness, and monotonicity. We show that these conditions are not vacuous and demonstrate with an example that they imply economically sensible restrictions on data consistent with laboratory observations. The reduced-form approach allows for a richer set of regular quantal response functions, which has proven useful for estimation purposes.
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Suggested Citation

  • Goeree, Jacob K. & Holt, Charles A. & Palfrey, Thomas R., 2004. "Regular quantal response equilibrium," Working Papers 1203, California Institute of Technology, Division of the Humanities and Social Sciences.
  • Handle: RePEc:clt:sswopa:1203
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    File URL: http://www.hss.caltech.edu/SSPapers/sswp1203c.pdf
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    References listed on IDEAS

    as
    1. McKelvey, Richard D & Palfrey, Thomas R, 1992. "An Experimental Study of the Centipede Game," Econometrica, Econometric Society, vol. 60(4), pages 803-836, July.
    2. Goeree, Jacob K. & Holt, Charles A. & Palfrey, Thomas R., 2002. "Quantal Response Equilibrium and Overbidding in Private-Value Auctions," Journal of Economic Theory, Elsevier, vol. 104(1), pages 247-272, May.
    3. Jacob K. Goeree & Charles A. Holt, 2001. "Ten Little Treasures of Game Theory and Ten Intuitive Contradictions," American Economic Review, American Economic Association, vol. 91(5), pages 1402-1422, December.
    4. Rosenthal, Robert W, 1989. "A Bounded-Rationality Approach to the Study of Noncooperative Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(3), pages 273-291.
    5. Chong, Juin-Kuan & Camerer, Colin F. & Ho, Teck H., 2006. "A learning-based model of repeated games with incomplete information," Games and Economic Behavior, Elsevier, vol. 55(2), pages 340-371, May.
    6. repec:wsi:wschap:9789813235816_0013 is not listed on IDEAS
    7. Anderson, Simon P. & Goeree, Jacob K. & Holt, Charles A., 2001. "Minimum-Effort Coordination Games: Stochastic Potential and Logit Equilibrium," Games and Economic Behavior, Elsevier, vol. 34(2), pages 177-199, February.
    8. 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.
    9. Charles A. Holt & Susan K. Laury, 2002. "Risk Aversion and Incentive Effects," American Economic Review, American Economic Association, vol. 92(5), pages 1644-1655, December.
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    11. Harless, David W & Camerer, Colin F, 1994. "The Predictive Utility of Generalized Expected Utility Theories," Econometrica, Econometric Society, vol. 62(6), pages 1251-1289, November.
    12. Simon P. Anderson & Jacob K. Goeree & Charles A. Holt, 1998. "Rent Seeking with Bounded Rationality: An Analysis of the All-Pay Auction," Journal of Political Economy, University of Chicago Press, vol. 106(4), pages 828-853, August.
    13. John D. Hey, 2018. "Why We Should Not Be Silent About Noise," World Scientific Book Chapters,in: Experiments in Economics Decision Making and Markets, chapter 13, pages 309-329 World Scientific Publishing Co. Pte. Ltd..
    14. 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.
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    16. Goeree, Jacob K. & Holt, Charles A. & Palfrey, Thomas R., 2003. "Risk averse behavior in generalized matching pennies games," Games and Economic Behavior, Elsevier, vol. 45(1), pages 97-113, October.
    17. 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.
    18. C. Monica Capra, 1999. "Anomalous Behavior in a Traveler's Dilemma?," American Economic Review, American Economic Association, vol. 89(3), pages 678-690, June.
    19. Philip A. Haile & Ali Horta├žsu & Grigory Kosenok, 2004. "On the Empirical Content of Quantal Response Models," Levine's Bibliography 122247000000000218, UCLA Department of Economics.
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