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Regular Quantal Response Equilibrium

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  • Jacob Goeree
  • Charles Holt
  • Thomas Palfrey

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 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. Copyright Springer Science + Business Media, Inc. 2005

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Bibliographic Info

Article provided by Springer in its journal Experimental Economics.

Volume (Year): 8 (2005)
Issue (Month): 4 (December)
Pages: 347-367

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Handle: RePEc:kap:expeco:v:8:y:2005:i:4:p:347-367

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Web page: http://www.springerlink.com/link.asp?id=102888

Related research

Keywords: quantal response equilibrium; discrete choice models; reduced-form approach;

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  1. Hey, John D & Orme, Chris, 1994. "Investigating Generalizations of Expected Utility Theory Using Experimental Data," Econometrica, Econometric Society, vol. 62(6), pages 1291-1326, November.
  2. Palfrey, Thomas R. & Goeree, Jacob & Holt, Charles, 2000. "Quantal Response Equilibrium and Overbidding in Private-value Auctions," Working Papers 1073, California Institute of Technology, Division of the Humanities and Social Sciences.
  3. Richard Mckelvey & Thomas Palfrey, 1998. "Quantal Response Equilibria for Extensive Form Games," Experimental Economics, Springer, vol. 1(1), pages 9-41, June.
  4. McKelvey, Richard D & Palfrey, Thomas R, 1992. "An Experimental Study of the Centipede Game," Econometrica, Econometric Society, vol. 60(4), pages 803-36, July.
  5. Harless, David W & Camerer, Colin F, 1994. "The Predictive Utility of Generalized Expected Utility Theories," Econometrica, Econometric Society, vol. 62(6), pages 1251-89, November.
  6. Jacob K. Goeree & Charles A. Holt, 2000. "Ten Little Treasures of Game Theory and Ten Intuitive Contradictions," Virginia Economics Online Papers 333, University of Virginia, Department of Economics.
  7. 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.
  8. 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.
  9. John Hey, 2005. "Why We Should Not Be Silent About Noise," Experimental Economics, Springer, vol. 8(4), pages 325-345, December.
  10. 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.
  11. Juin-Kuan Chong & Colin F. Camerer & Teck H. Ho, 2005. "A learning-based model of repeated games with incomplete information," Levine's Bibliography 666156000000000537, UCLA Department of Economics.
  12. 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.
  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, 06.
  14. C. Monica Capra, 1999. "Anomalous Behavior in a Traveler's Dilemma?," American Economic Review, American Economic Association, vol. 89(3), pages 678-690, June.
  15. 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.
  16. Rosenthal, Robert W, 1989. "A Bounded-Rationality Approach to the Study of Noncooperative Games," International Journal of Game Theory, Springer, vol. 18(3), pages 273-91.
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