The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Quantal Response Equilibria

  • Jacob K. Goeree
  • Charles A. Holt
  • Thomas R. Palfrey
Reference work entry


A quantal response specifies choice probabilities that are smooth, increasing functions of expected payoffs. A quantal response equilibrium has the property that the choice distributions match the belief distributions used to calculate expected payoffs. This stochastic generalization of the Nash equilibrium provides strong empirical restrictions that are generally consistent with data from laboratory experiments with human subjects. We define the concept of regular quantal response equilibrium and discuss several applications from the recent literature.


Coordination Extensive form games Fixed-point theorems Incomplete information Interchangeability Learning Nash equilibrium Probabilistic choice models Quantal response equilibrium Sequential equilibria Traveller’s Dilemma 

JEL Classification

This is a preview of subscription content, log in to check access.



We acknowledge financial support from the Alfred P. Sloan Foundation, the National Science Foundation (SBR 0094800 and 0551014; SES 0450712 and 0214013), and the Dutch National Science Foundation (VICI 453.03.606).


  1. Anderson, S.K., J.K. Goeree, and C.A. Holt. 2001. Minimum effort coordination games: Stochastic potential and the logit equilibrium. Games and Economic Behavior 34: 177–199.CrossRefGoogle Scholar
  2. Capra, C.M., J.K. Goeree, R. Gomez, and C.A. Holt. 1999. Anomalous behavior in a traveler’s dilemma? American Economic Review 89: 678–690.CrossRefGoogle Scholar
  3. Cason, T.N., and M. Van Lam. 2005. Uncertainty and resistance to reform in laboratory participation games. European Journal of Political Economy 21: 708–737.CrossRefGoogle Scholar
  4. Goeree, J.K., and C.A. Holt. 2001. Ten little treasures of game theory and ten intuitive contradictions. American Economic Review 91: 1402–1422.CrossRefGoogle Scholar
  5. Goeree, J.K., and C.A. Holt. 2005a. An experimental study of costly coordination. Games and Economic Behavior 46: 281–294.Google Scholar
  6. Goeree, J.K., and C.A. Holt. 2005b. An explanation of anomalous behavior in models of political participation. American Political Science Review 99: 201–213.CrossRefGoogle Scholar
  7. Goeree, J.K., C.A. Holt, and T.R. Palfrey. 2002. Quantal response equilibrium and overbidding in private-value auctions. Journal of Economic Theory 104: 247–272.CrossRefGoogle Scholar
  8. Goeree, J.K., C.A. Holt, and T.R. Palfrey. 2003. Risk averse behavior in asymmetric matching pennies games. Games and Economic Behavior 45: 97–113.CrossRefGoogle Scholar
  9. Goeree, J.K., C.A. Holt, and T.R. Palfrey. 2005. Regular quantal response equilibrium. Experimental Economics 8: 347–367.CrossRefGoogle Scholar
  10. Guarnaschelli, S., R.D. McKelvey, and T.R. Palfrey. 2000. An experimental study of jury decision rules. American Political Science Review 94: 407–423.CrossRefGoogle Scholar
  11. Haile, P., A. Hortacsu. and G. Kosenok. 2006. On the empirical content of quantal response equilibrium. Working paper. Yale School of Management, Yale University.Google Scholar
  12. Harsanyi, J. 1973. Games with randomly disturbed payoffs: A new rationale for mixed strategy equilibrium. International Journal of Game Theory 2: 1–23.CrossRefGoogle Scholar
  13. Levine, D., and T.R. Palfrey. 2007. The paradox of voter participation: An experimental study. American Political Science Review 101: 143–158.CrossRefGoogle Scholar
  14. McFadden, D. 1974. Conditional logit analysis of qualitative choice behavior. In Frontiers in econometrics, ed. P. Zarembka. New York: Academic.Google Scholar
  15. McKelvey, R.D., and T.R. Palfrey. 1995. Quantal response equilibrium for normal form games. Games and Economic Behavior 10: 6–38.CrossRefGoogle Scholar
  16. McKelvey, R.D., and T.R. Palfrey. 1996. A statistical theory of equilibrium in games. Japanese Economic Review 47: 186–209.CrossRefGoogle Scholar
  17. McKelvey, R.D., and T.R. Palfrey. 1998. Quantal response equilibrium for extensive form games. Experimental Economics 1: 9–41.CrossRefGoogle Scholar
  18. McKelvey, R.D., T.R. Palfrey, and R. Weber. 2000. The effects of payoff magnitude and heterogeneity on behavior in 2 × 2 games with a unique mixed-strategy equilibrium. Journal of Economic Behavior and Organization 42: 523–548.CrossRefGoogle Scholar
  19. Ochs, J. 1995. Games with unique, mixed strategy equilibria: An experimental study. Games and Economic Behavior 10: 202–217.CrossRefGoogle Scholar

Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Jacob K. Goeree
    • 1
  • Charles A. Holt
    • 1
  • Thomas R. Palfrey
    • 1
  1. 1.