scholarly journals Stationary Concepts for Experimental 2 × 2 Games: Comment

2011 ◽  
Vol 101 (2) ◽  
pp. 1029-1040 ◽  
Author(s):  
Christoph Brunner ◽  
Colin F Camerer ◽  
Jacob K Goeree
Keyword(s):  
Nash Equilibrium ◽  
Loss Aversion ◽  
The Other ◽  
Quantal Response ◽  
Quantal Response Equilibrium ◽  
Equilibrium Payoff ◽  
Laboratory Results ◽  
Impulse Balance

Reinhard Selten and Thorsten Chmura (2008) recently reported laboratory results for completely mixed 2 X 2 games used to compare Nash equilibrium with four other stationary concepts: quantal response equilibrium, action-sampling equilibrium, payoff-sampling equilibrium, and impulse balance equilibrium. We reanalyze their data, correct some errors, and find that Nash clearly fits worst while the four other concepts perform about equally well. We also report new analysis of other previous experiments that illustrate the importance of the loss aversion hardwired into impulse balance equilibrium: when the other non-Nash concepts are augmented with loss aversion, they outperform impulse balance equilibrium.

scholarly journals Stationary Concepts for Experimental 2x2-Games

2008 ◽  
Vol 98 (3) ◽  
pp. 938-966 ◽  
Author(s):  
Reinhard Selten ◽  
Thorsten Chmura
Keyword(s):  
Nash Equilibrium ◽  
Subject Group ◽  
Quantal Response ◽  
Random Matching ◽  
Quantal Response Equilibrium ◽  
Equilibrium Payoff ◽  
Impulse Balance

Five stationary concepts for completely mixed 2x2-games are experimentally compared: Nash equilibrium, quantal response equilibrium, action-sampling equilibrium, payoff-sampling equilibrium (Martin J. Osborne and Ariel Rubinstein 1998), and impulse balance equilibrium. Experiments on 12 games, 6 constant sum games, and 6 nonconstant sum games were run with 12 independent subject groups for each constant sum game and 6 independent subject groups for each nonconstant sum game. Each independent subject group consisted of four players 1 and four players 2, interacting anonymously over 200 periods with random matching. The comparison of the five theories shows that the order of performance from best to worst is as follows: impulse balance equilibrium, payoff-sampling equilibrium, action-sampling equilibrium, quantal response equilibrium, Nash equilibrium. (JEL C70, C91)

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 Stationary Concepts for Experimental 2 × 2 Games: Reply

2011 ◽  
Vol 101 (2) ◽  
pp. 1041-1044 ◽  
Author(s):  
Reinhard Selten ◽  
Thorsten Chmura ◽  
Sebastian J Goerg
Keyword(s):  
Experimental Studies ◽  
Quantal Response ◽  
Quantal Response Equilibrium ◽  
New Findings ◽  
Computational Errors ◽  
Impulse Balance ◽  
Better Than ◽  
Non Parametric

This is a reply to “Stationary Concepts for Experimental 2 X 2 Games: Comment” by Brunner, Camerer, and Goeree which corrects some computational errors in Selten and Chmura (2008) and extends the comparison of five stationary concepts to data from previous experimental studies. We critically discuss their new findings and relate them to the data of Selten and Chmura (2008). We conclude that the parametric concepts of action-sampling equilibrium and payoff-sampling equilibrium perform better than quantal response equilibrium, and that the non-parametric concept of impulse-balance equilibrium performs at least as well as quantal response equilibrium. (JEL C70)

scholarly journals Quantal Response Equilibrium

2016 ◽  
Author(s):  
Jacob K. Goeree ◽  
Charles A. Holt ◽  
Thomas R. Palfrey
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Rational Expectations ◽  
Stochastic Theory ◽  
Quantal Response ◽  
Quantal Response Equilibrium ◽  
Wide Audience ◽  
Science Management ◽  
Classical Game ◽  
Classical Game Theory

This book presents a stochastic theory of games that unites probabilistic choice models developed in psychology and statistics with the Nash equilibrium approach of classical game theory. Nash equilibrium assumes precise and perfect decision making in games, but human behavior is inherently stochastic and people realize that the behavior of others is not perfectly predictable. In contrast, quantal response equilibrium models choice behavior as probabilistic and extends classical game theory into a more realistic and useful framework with broad applications for economics, political science, management, and other social sciences. This book spans the range from basic theoretical foundations to examples of how the principles yield useful predictions and insights in strategic settings, including voting, bargaining, auctions, public goods provision, and more. The approach provides a natural framework for estimating the effects of behavioral factors like altruism, reciprocity, risk aversion, judgment fallacies, and impatience. New theoretical results push the frontiers of models that include heterogeneity, learning, and well-specified behavioral modifications of rational choice and rational expectations. The empirical relevance of the theory is enhanced by discussion of data from controlled laboratory experiments, along with a detailed users' guide for estimation techniques. The book makes pioneering game-theoretic methods and interdisciplinary applications available to a wide audience.

A Refinement of Logit Quantal Response Equilibrium

2018 ◽  
Vol 20 (02) ◽  
pp. 1850004
Author(s):  
Pavlo Blavatskyy
Keyword(s):  
Nash Equilibrium ◽  
Utility Function ◽  
Equilibrium Solution ◽  
Solution Concept ◽  
Affine Transformations ◽  
Quantal Response ◽  
Quantal Response Equilibrium ◽  
Von Neumann ◽  
Proposed Modification ◽  
Simultaneous Move

Unlike the Nash equilibrium, logit quantal response equilibrium is affected by positive affine transformations of players’ von Neumann–Morgenstern utility payoffs. This paper presents a modification of a logit quantal response equilibrium that makes this equilibrium solution concept invariant to arbitrary normalization of utility payoffs. Our proposed modification can be viewed as a refinement of logit quantal response equilibria: instead of obtaining a continuum of equilibria (for different positive affine transformations of utility function) we now obtain only one equilibrium for all possible positive affine transformations of utility function. We define our refinement for simultaneous-move noncooperative games in the normal form.

scholarly journals Bounded rational response equilibria in human sensorimotor interactions

2021 ◽  
Vol 288 (1962) ◽  
Author(s):  
Cecilia Lindig-León ◽  
Gerrit Schmid ◽  
Daniel A. Braun
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Nash Solution ◽  
Quantal Response ◽  
Quantal Response Equilibrium ◽  
Economic Decision Making ◽  
Sensorimotor Interactions ◽  
The Nash Solution ◽  
Special Case ◽  
General Tool

The Nash equilibrium is one of the most central solution concepts to study strategic interactions between multiple players and has recently also been shown to capture sensorimotor interactions between players that are haptically coupled. While previous studies in behavioural economics have shown that systematic deviations from Nash equilibria in economic decision-making can be explained by the more general quantal response equilibria, such deviations have not been reported for the sensorimotor domain. Here we investigate haptically coupled dyads across three different sensorimotor games corresponding to the classic symmetric and asymmetric Prisoner's Dilemma, where the quantal response equilibrium predicts characteristic shifts across the three games, although the Nash equilibrium stays the same. We find that subjects exhibit the predicted deviations from the Nash solution. Furthermore, we show that taking into account subjects' priors for the games, we arrive at a more accurate description of bounded rational response equilibria that can be regarded as a quantal response equilibrium with non-uniform prior. Our results suggest that bounded rational response equilibria provide a general tool to explain sensorimotor interactions that include the Nash equilibrium as a special case in the absence of information processing limitations.

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