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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: rdm@hss.caltech.edu, trp@hss.caltech.edu
email: rdm@hss.caltech.edu, trp@hss.caltech.edu
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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

Information

Type
Research Article
Information
Experimental Economics , Volume 1 , Issue 1 , June 1998 , pp. 9 - 41
Copyright
Copyright © 1998 Economic Science Association

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