Hostname: page-component-7b9c58cd5d-g9frx Total loading time: 0 Render date: 2025-03-15T11:33:57.855Z Has data issue: false hasContentIssue false
  • English
  • Français

Quantal Response Equilibria for Extensive Form Games

Published online by Cambridge University Press:  14 March 2025

Richard D. McKelvey  and
Thomas R. Palfrey
Richard D. McKelvey*
Affiliation:
Division of the Humanities and Social Sciences, California Institute of Technology, Pasadena, CA 91125, USA
Thomas R. Palfrey*
Affiliation:
Division of the Humanities and Social Sciences, California Institute of Technology, Pasadena, CA 91125, USA
*
email: [email protected], [email protected]
email: [email protected], [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This article investigates the use of standard econometric models for quantal choice to study equilibria of extensive form games. Players make choices based on a quantal-choice model and assume other players do so as well. We define an agent quantal response equilibrium (AQRE), which applies QRE to the agent normal form of an extensive form game and imposes a statistical version of sequential rationality. We also define a parametric specification, called logit-AQRE, in which quantal-choice probabilities are given by logit response functions. AQRE makes predictions that contradict the invariance principle in systematic ways. We show that these predictions match up with some experimental findings by Schotter et al. (1994) about the play of games that differ only with respect to inessential transformations of the extensive form. The logit-AQRE also implies a unique selection from the set of sequential equilibria in generic extensive form games. We examine data from signaling game experiments by Banks et al. (1994) and Brandts and Holt(1993). We find that the logit-AQRE selection applied to these games succeeds in predicting patterns of behavior observed in these experiments, even when our prediction conflicts with more standard equilibrium refinements, such as the intuitive criterion. We also reexamine data from the McKelvey and Palfrey (1992) centipede experiment and find that the AQRE model can account for behavior that had previously been explained in terms of altruistic behavior.

Keywords

game theoryexperimental economicsquantal response equilibrium

JEL classification

C70: General C92: Laboratory, Group Behavior C72: Noncooperative Games
Type
Research Article
Information
Experimental Economics , Volume 1 , Issue 1 , June 1998 , pp. 9 - 41
Copyright
Copyright © 1998 Economic Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anderson, S., Goeree, J., and Holt, C. (1998). “Rent Seeking with Bounded Rationality: An Analysis of the All Pay Auction.” forthcoming in the Journal of Political Economy.CrossRefGoogle Scholar
Banks, J., Camerer, C., and Porter, D. (1994). “Experimental Tests of Nash Refinements in Signaling Games.” Games and Economic Behavior. 6, 1–31.CrossRefGoogle Scholar
Brandts, J. and Holt, C.A. (1992). “An Experimental Test of Equilibrium Dominance in Signaling Games.” American Economic Review. 82, 1350–1365.Google Scholar
Brandts, J. and Holt, C.A. (1993). “Adjustment Patterns and Equilibrium Selection in Experimental Signaling Games.” International Journal of Game Theory. 22, 279–302.CrossRefGoogle Scholar
Chen, H., Friedman, J.W., and Thisse, J. (1997). “Boundedly Rational Nash Equilibrium: A Probabilistic Choice Approach.” Games and Economic Behavior. 18, 32–54.CrossRefGoogle Scholar
Chen, K.-Y (1994). “The Strategic Behavior of Rational Novices.” Ph.D. dissertation, California Institute of Technology.Google Scholar
Cooper, R., DeJong, D., Forsythe, R., and Ross, T. (1989). “Communication in the Battle of the Sexes Game: Some Experimental Results.” RAND Journal of Economics. 20, 568–587.CrossRefGoogle Scholar
Cooper, R., DeJong, D., Forsythe, R., and Ross, T. (1990). “Selection Criteria in Coordination Games: Some Experimental Results.” American Economic Review. 80, 218–233.Google Scholar
Fey, M., McKelvey, R.D., and Palfrey, T.R. (1996). “Experiments on the Constant-Sum Centipede Game.” International Journal of Game Theory. 25, 269–287.CrossRefGoogle Scholar
Gale, J., Binmore, K., and Samuelson, L. (1995). “Learning to be Imperfect: The Ultimatum Game.” Games and Economic Behavior. 8, 56–90.CrossRefGoogle Scholar
Guillemin, V. and Pollack, A. (1974). Differential Topology. Prentice-Hall.Google Scholar
Harsanyi, J. (1973). “Games with Randomly Disturbed Payoffs.” International Journal of Game Theory. 2, 1–23.CrossRefGoogle Scholar
Harsanyi, J. and Selten, R. (1988). A General Theory of Equilibrium Selection in Games. Cambridge, MA: MIT Press.Google Scholar
Kohlberg, E. and Mertens, J.-F. (1986). “On the Strategic Stability of Equilibria.” Econometrica. 54, 1003–1037.CrossRefGoogle Scholar
Kreps, D. and Wilson, R. (1982). “Reputation and Imperfect Information.” Journal of Economic Theory. 27, 253–279.CrossRefGoogle Scholar
Lopez, G. (1995). “Quantal Response Equilibria for Models of Price Competition.” Ph.D. dissertation, University of Virginia.Google Scholar
Luce, D. (1959). Individual Choice Behavior. New York: Wesley.Google Scholar
McFadden, D. (1974). “Conditional Logit Analysis of Qualitative Choice Behavior.” In Zarembka, P. (ed.), Frontiers in Econometrics. New York: Academic Press.Google Scholar
McKelvey, R.D. and Palfrey, T.R. (1992). “An Experimental Study of the Centipede Game.” Econometrica. 60, 803–836.CrossRefGoogle Scholar
McKelvey, R.D. and Palfrey, T.R. (1995). “Quantal Response Equilibria in Normal Form Games.” Games and Economic Behavior. 7, 6–38.CrossRefGoogle Scholar
McKelvey, R.D. and Palfrey, T.R. (1996). “A Statistical Theory of Equilibrium in Games.” Japanese Economic Review. 47, 186–209.CrossRefGoogle Scholar
Partow, J. and Schotter, A. (1993). “Does Game Theory Predict Well for the Wrong Reasons? An Experimental Investigation.” C.V. Starr Center for Applied Economics Working Paper 93-46, New York University.Google Scholar
Rosenthal, R. (1989). “A Bounded-Rationality Approach to the Study of Noncooperative Games.” International Journal of Game Theory. 18, 273–292.CrossRefGoogle Scholar
Schotter, A., Weigelt, K., and Wilson, C. (1994). “A Laboratory Investigation of Multiperson Rationality and Presentation Effects.” Games and Economic Behavior. 6, 445–468.CrossRefGoogle Scholar
Van Damme, E. (1987). Stability and Perfection of Nash Equilibria Berlin: Springer-Verlag.CrossRefGoogle Scholar
Zauner, K. (1993). “Bubbles, Speculation, and a Reconsideration of the Centipede Game Experiment.” Mimeo, University of California at San Diego. Revised as “A Reconsideration of the Centipede Game Experiments”.Google Scholar