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Quantal Response EquilibriumA Stochastic Theory of Games$
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Jacob K. Goeree, Charles A. Holt, and Thomas R. Palfrey

Print publication date: 2016

Print ISBN-13: 9780691124230

Published to Princeton Scholarship Online: January 2018

DOI: 10.23943/princeton/9780691124230.001.0001

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Quantal Response Equilibrium in Normal-Form Games

Quantal Response Equilibrium in Normal-Form Games

(p.10) 2 Quantal Response Equilibrium in Normal-Form Games
Quantal Response Equilibrium

Jacob K. Goeree

Charles A. Holt

Thomas R. Palfrey

Princeton University Press

This chapter lays out the general theory of quantal response equilibrium (QRE) for normal-form games. It starts with the reduced-form approach to QR, based on the direct specification of “regular” quantal or smoothed best-response functions required to satisfy four intuitive axioms of stochastic choice. A simple asymmetric matching pennies game is used to illustrate these ideas and show that QRE imposes strong restrictions on the data, even without parametric assumptions on the quantal response functions. Particular attention is given to the logit QRE, since it is the most commonly used approach taken when QRE is applied to experimental or other data. The discussion includes the topological and limiting properties of logit QRE and connections with refinement concepts. QRE is also related to several other equilibrium models of imperfectly rational behavior in games, including a game-theoretic equilibrium version of Luce's (1959) model of individual choice, Rosenthal's (1989) linear response model, and Van Damme's (1987) control cost model; these connections are explained in the chapter.

Keywords:   quantal response equilibrium, QRE, normal-form games, reduced-form approach, logit QRE, imperfectly rational behavior

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