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Regular Quantal Response Equilibrium

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Author Info
Jacob Goeree
Charles Holt
Thomas Palfrey

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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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File URL: http://hdl.handle.net/10.1007/s10683-005-5374-7
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Publisher 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

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

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. McKelvey, Richard D & Palfrey, Thomas R, 1992. "An Experimental Study of the Centipede Game," Econometrica, Econometric Society, vol. 60(4), pages 803-36, July. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
    Other versions:
  3. 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. [Downloadable!]
    Other versions:
  4. 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. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
  6. 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.
  7. Richard Mckelvey & Thomas Palfrey, 1998. "Quantal Response Equilibria for Extensive Form Games," Experimental Economics, Springer, vol. 1(1), pages 9-41, June. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  9. 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. [Downloadable!] (restricted)
  10. C. Monica Capra et al., 1999. "Anomalous Behavior in a Traveler's Dilemma?," American Economic Review, American Economic Association, vol. 89(3), pages 678-690, June. [Downloadable!] (restricted)
  11. 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. [Downloadable!]
  12. 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. [Downloadable!] (restricted)
  13. 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. [Downloadable!] (restricted)
  14. John Hey, 2005. "Why We Should Not Be Silent About Noise," Experimental Economics, Springer, vol. 8(4), pages 325-345, December. [Downloadable!] (restricted)
  15. Philip A. Haile & Ali Hortaçsu & Grigory Kosenok, 2004. "On the Empirical Content of Quantal Response Models," Levine's Bibliography 122247000000000218, UCLA Department of Economics. [Downloadable!]
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Carrillo, Juan D. & Palfrey, Thomas R., 2006. "The compromise game: Two-sided adverse selection in the laboratory," Working Papers 1259, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
  2. Glenn W Harrison, 2008. "Neuroeconomics: A Critical Reconsideration," Levine's Working Paper Archive 122247000000001915, David K. Levine. [Downloadable!]
  3. Philip A. Haile & Ali Hortacsu & Grigory Kosenok, 0820. "On the Empirical Content of Quantal Response Equilibrium," Cowles Foundation Discussion Papers 1432R, Cowles Foundation, Yale University, revised Jun 0820. [Downloadable!]
    Other versions:
  4. Jonathan W. Leland, 2006. "Equilibrium Selection, Similarity Judgments and the“Nothing to Gain/Nothing to Lose”Effect," Levine's Working Paper Archive 321307000000000378, David K. Levine. [Downloadable!]
    Other versions:
  5. Jacob K. Goeree & Thomas R. Palfrey & Brian W. Rogers & Richard D. McKelvey, 2006. "Self-Correcting Information Cascades," Levine's Bibliography 321307000000000211, UCLA Department of Economics. [Downloadable!]
    Other versions:
  6. Jeremy T. Fox, 2009. "Identification in Matching Games," NBER Working Papers 15092, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  7. Juan D. Carrillo & Thomas R. Palfrey, 2007. "The Compromise Game: Two-sided Adverse Selection in the Laboratory," Levine's Bibliography 321307000000000754, UCLA Department of Economics. [Downloadable!]
  8. Juan D Carrillo & Thomas R Palfrey, 2007. "The Compromise Game: Two-Sided Adverse Selection in the Laboratory," Levine's Bibliography 122247000000001463, UCLA Department of Economics. [Downloadable!]
  9. Jonathan E. Alevy & Michael S. Haigh & John List, 2006. "Information Cascades: Evidence from An Experiment with Financial Market Professionals," NBER Working Papers 12767, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  10. Miguel A Costa-Gomes & Vincent P Crawford & Nagore Iriberri, 2008. "Comparing Models of Strategic Thinking in Van Huyck, Battalio, and Beil’s Coordination Games," Levine's Bibliography 122247000000002346, UCLA Department of Economics. [Downloadable!]
  11. Graham Loomes, 2005. "Modelling the Stochastic Component of Behaviour in Experiments: Some Issues for the Interpretation of Data," Experimental Economics, Springer, vol. 8(4), pages 301-323, December. [Downloadable!] (restricted)
  12. Camerer, Colin F. & Palfrey, Thomas R. & Rogers, Brian W., 2006. "Heterogeneous quantal response equilibrium and cognitive hierarchies," Working Papers 1260, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
  13. Jeremy T. Fox, 2008. "Estimating Matching Games with Transfers," NBER Working Papers 14382, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  14. Carrillo, Juan D & Palfrey, Thomas R, 2007. "The Compromise Game: Two-sided Adverse Selection in the Laboratory," CEPR Discussion Papers 6103, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
  15. Colin F. Camerer & Thomas R. Palfrey & Brian W. Rogers, 2006. "Heterogeneous Quantal Response Equilibrium," Levine's Bibliography 321307000000000193, UCLA Department of Economics. [Downloadable!]
  16. Thomas R. Palfrey, 2006. "The Compromise Game: Two-sided Adverse Selection in the Laboratory," IEPR Working Papers 06.60, Institute of Economic Policy Research (IEPR). [Downloadable!]
  17. Boone, J. & Müller, W. & Suetens, S., 2009. "Naked Exclusion: Towards a Behavioral Approach to Exclusive Dealing," Discussion Paper 2009-30, Tilburg University, Center for Economic Research. [Downloadable!]
    Other versions:
  18. Voorneveld, Mark & Fagraeus Lundström, Helena, 2005. "Strategic equivalence and bounded rationality in extensive form games," Working Paper Series in Economics and Finance 605, Stockholm School of Economics. [Downloadable!]
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