Bayesian Inference for Quantal Response Equilibrium in Normal-Form Games

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.

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Quantal response methods for equilibrium selection in normal form games

Journal of Mathematical Economics ◽

10.1016/j.jmateco.2016.04.003 ◽

2016 ◽

Vol 64 ◽

pp. 113-123 ◽

Cited By ~ 2

Author(s):

Boyu Zhang

Keyword(s):

Normal Form ◽

Equilibrium Selection ◽

Quantal Response ◽

Normal Form Games

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On the Empirical Content of Quantal Response Equilibrium

The American Economic Review ◽

10.1257/aer.98.1.180 ◽

2008 ◽

Vol 98 (1) ◽

pp. 180-200 ◽

Cited By ~ 103

Author(s):

Philip A Haile ◽

Ali Hortaçsu ◽

Grigory Kosenok

Keyword(s):

Normal Form ◽

A Priori ◽

Empirical Content ◽

Quantal Response ◽

Quantal Response Equilibrium ◽

Form Game ◽

Normal Form Game ◽

Experimental Subjects ◽

Observed Behavior

The quantal response equilibrium (QRE) notion of Richard D. McKelvey and Thomas R. Palfrey (1995) has recently attracted considerable attention, due in part to its widely documented ability to rationalize observed behavior in games played by experimental subjects. However, even with strong a priori restrictions on unobservables, QRE imposes no falsifiable restrictions: it can rationalize any distribution of behavior in any normal form game. After demonstrating this, we discuss several approaches to testing QRE under additional maintained assumptions. (JEL C72, D84)

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