Quantal Response Equilibrium in Normal-Form Games

2016 ◽  
Author(s):  
Jacob K. Goeree ◽  
Charles A. Holt ◽  
Thomas R. Palfrey
Keyword(s):  
Normal Form ◽  
Cost Model ◽  
Reduced Form ◽  
Individual Choice ◽  
Response Functions ◽  
Quantal Response ◽  
Quantal Response Equilibrium ◽  
Control Cost ◽  
Normal Form Games ◽  
Best Response

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.

scholarly journals A Generalization of Quantal Response Equilibrium via Perturbed Utility

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 20
Author(s):  
Roy Allen ◽  
John Rehbeck
Keyword(s):  
Response Function ◽  
Expected Utility ◽  
Reduced Form ◽  
Limited Attention ◽  
Nested Logit ◽  
Quantal Response ◽  
Quantal Response Equilibrium ◽  
Best Response ◽  
Utility Preferences

We present a tractable generalization of quantal response equilibrium via non-expected utility preferences. In particular, we introduce concave perturbed utility games in which an individual has strategy-specific utility indices that depend on the outcome of the game and an additively separable preference to randomize. The preference to randomize can be viewed as a reduced form of limited attention. Using concave perturbed utility games, we show how to enrich models based on logit best response that are common from quantal response equilibrium. First, the desire to randomize can depend on opponents’ strategies. Second, we show how to derive a nested logit best response function. Lastly, we present tractable quadratic perturbed utility games that allow complementarity.

Heterogeneity

2016 ◽  
Author(s):  
Jacob K. Goeree ◽  
Charles A. Holt ◽  
Thomas R. Palfrey
Keyword(s):  
Choice Behavior ◽  
Error Rates ◽  
The Other ◽  
Individual Heterogeneity ◽  
Response Functions ◽  
Quantal Response ◽  
Quantal Response Equilibrium ◽  
Skill Levels ◽  
Apparent Reason ◽  
Chess Players

Players have different skills, which has implications for the degree to which they make errors. Low-skill hitters in baseball often swing at bad pitches, beginning skiers frequently fall for no apparent reason, and children often lose at tic-tac-toe. At the other extreme, there are brilliant chess players, bargainers, and litigators who seem to know exactly what move to make or offer to decline. From a quantal response equilibrium (QRE) perspective, these skill levels can be modeled in terms of variation in error rates or in responsiveness of quantal response functions. This chapter explores issues related to individual heterogeneity with respect to player error rates. It also describes some extensions of QRE that relax the assumption that player expectations about the choice behavior of other players are correct. For example, in games that are played only once, players are not able to learn from others' prior decisions, and expectations must be based on introspection. The chapter develops the implications of noisy introspection embedded in a model of iterated thinking.

scholarly journals On the Empirical Content of Quantal Response Equilibrium

2008 ◽  
Vol 98 (1) ◽  
pp. 180-200 ◽  
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)

scholarly journals The refined best-response correspondence in normal form games

2014 ◽  
Vol 44 (1) ◽  
pp. 165-193 ◽  
Author(s):  
Dieter Balkenborg ◽  
Josef Hofbauer ◽  
Christoph Kuzmics
Keyword(s):  
Normal Form ◽  
Normal Form Games ◽  
Best Response ◽  
Best Response Correspondence
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