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Published December 2005 | Submitted
Journal Article Open

Regular Quantal Response Equilibrium


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.

Additional Information

© 2005 Economic Science Association. Received June 27, 2004; Revised June 2, 2005; Accepted July 27, 2005. Financial support from the National Science Foundation NSF (SBR-0098400 and SES-0079301) and the Alfred P. Sloan Foundation is gratefully acknowledged. The paper has benefitted from discussions with Michelle Goeree, Philip Haile, Ali Hortacsu, David Levine, Angela Moore, Brian Rogers and Larry Samuelson. The Haile et al. (2004) paper inspired us to think more deeply about the restrictions implied by QRE models. We also acknowledge helpful comments from seminar participants at the 2003 ESA North American Meeting and the Nottingham workshop on "The Role of Experimental Methods in Economics," an anonymous referee and the associate editors for this special issue.

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