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Published August 18, 2017 | Submitted
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Quantal Response Equilibria for Extensive Form Games


This paper 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, Weigelt and Wilson (1993) 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 subgame perfect equilibria in generic extensive form games. We examine data from signalling game experiments by Banks, Camerer, and Porter (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.

Additional Information

This paper has benefited from comments by participants at the Conference on Learning in Games (Texas A&M University, February 1994) and the European Meetings of the Econometric Society (Maastricht, September 1994). We thank the participants for their comments and also thank Peter Coughlan, Mark Fey, Eugene Grayver, and Rob Weber for their research assistance. The financial support of the National Science Foundation (Grant #SBR-9223701) is gratefully acknowledged. Published as McKelvey, Richard D., and Thomas R. Palfrey. "Quantal response equilibria for extensive form games." Experimental economics 1, no. 1 (1998): 9-41.

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