Quantal Response Methods for Equilibrium Selection in Normal Form Games
Quantal Response Methods for Equilibrium Selection in Normal Form Games

Author: Boyu Zhang

Publisher:

Published: 2014

Total Pages: 45

ISBN-13:

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This paper describes a general framework for equilibrium selection by tracing the graph of the quantal response equilibrium (QRE) correspondence as a function of the estimation error. If a quantal response function satisfies C2 continuity, monotonicity and cumulativity, the graph of QRE correspondence generically includes a unique branch that starts at the centroid of the strategy simplex and converges to a unique Nash equilibrium as noises vanish. This equilibrium is called the limiting QRE of the game. We then provide sufficient conditions for the limiting QRE in normal form games, J×J symmetric games and J×J bimatrix games. Based on these conditions, the effects of payoff transformations and adding/eliminating dominated strategies on equilibrium selection are investigated. We find that in J×J symmetric games, any strict Nash equilibrium can be selected as the limiting QRE by appropriately adding a single strictly dominated strategy.

Quantal Response Equilibrium with Symmetry
Quantal Response Equilibrium with Symmetry

Author: Evan Friedman

Publisher:

Published: 2022

Total Pages: 0

ISBN-13:

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We study an axiomatic variant of quantal response equilibrium (QRE) for normal form games that augments the regularity axioms (Goeree et al., 2005) with various forms of “symmetry” across players and actions. The model refines regular QRE, generalizes logit QRE, and is tractable in many applications. The main result is a representation theorem that characterizes the model's set-valued predictions by taking unions and intersections of simple sets. We completely characterize the predictions for (almost) all 2x2 games, a corollary of which is to show, in co- ordination games, which Nash equilibrium is selected by the principal branch of the logit correspondence. As applications, we consider three classic games: public goods provision with heterogenous costs of participation, jury voting with unanimity, and the infinitely repeated prisoner's dilemma. For each, we characterize all equilibria within a particular large class. An analysis of existing experiments shows the model's potential for organizing experimental data.

Quantal Response Equilibrium
Quantal Response Equilibrium

Author: Jacob K. Goeree

Publisher: Princeton University Press

Published: 2016-06-28

Total Pages: 322

ISBN-13: 069112423X

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Quantal Response Equilibrium 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, QRE 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. Quantal Response Equilibrium 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. Quantal Response Equilibrium makes pioneering game-theoretic methods and interdisciplinary applications available to a wide audience.

Quantal Response Equilibrium
Quantal Response Equilibrium

Author: Jacob K. Goeree

Publisher: Princeton University Press

Published: 2016-06-28

Total Pages: 328

ISBN-13: 1400880920

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Quantal Response Equilibrium 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, QRE 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. Quantal Response Equilibrium 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. Quantal Response Equilibrium makes pioneering game-theoretic methods and interdisciplinary applications available to a wide audience.

An Application of Decision Theoretical Models of Probabilistic Choice to Solving 2x2 Simultaneous-Move Noncooperative Games in the Normal Form
An Application of Decision Theoretical Models of Probabilistic Choice to Solving 2x2 Simultaneous-Move Noncooperative Games in the Normal Form

Author: Pavlo R. Blavatskyy

Publisher:

Published: 2013

Total Pages: 0

ISBN-13:

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Several models of probabilistic choice under uncertainty allow for deterministic choice if one act state-wise dominates the other. Such models have a natural application in game theory where probabilistic choice corresponds to mixed strategies, deterministic choice -- to pure strategies and state-wise dominance -- to strategic dominance. This paper considers an application to the simplest possible 2x2 simultaneous-move noncooperative game in the normal form. We derive a new equilibrium solution concept that coincides with the standard Nash equilibrium in pure strategies but resembles a quantal response equilibrium in mixed strategies. In particular, players randomize between strategies not in order to keep their opponent indifferent between his or her strategies (as in the mixed strategy Nash equilibrium) but because they are more likely to (but not always) choose strategies yielding higher utility.

Evolutionary Game Dynamics
Evolutionary Game Dynamics

Author: American Mathematical Society. Short Course

Publisher: American Mathematical Soc.

Published: 2011-10-27

Total Pages: 186

ISBN-13: 0821853260

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This volume is based on lectures delivered at the 2011 AMS Short Course on Evolutionary Game Dynamics, held January 4-5, 2011 in New Orleans, Louisiana. Evolutionary game theory studies basic types of social interactions in populations of players. It combines the strategic viewpoint of classical game theory (independent rational players trying to outguess each other) with population dynamics (successful strategies increase their frequencies). A substantial part of the appeal of evolutionary game theory comes from its highly diverse applications such as social dilemmas, the evolution of language, or mating behaviour in animals. Moreover, its methods are becoming increasingly popular in computer science, engineering, and control theory. They help to design and control multi-agent systems, often with a large number of agents (for instance, when routing drivers over highway networks or data packets over the Internet). While these fields have traditionally used a top down approach by directly controlling the behaviour of each agent in the system, attention has recently turned to an indirect approach allowing the agents to function independently while providing incentives that lead them to behave in the desired way. Instead of the traditional assumption of equilibrium behaviour, researchers opt increasingly for the evolutionary paradigm and consider the dynamics of behaviour in populations of agents employing simple, myopic decision rules.

A Refinement of Logit Quantal Response Equillibrium
A Refinement of Logit Quantal Response Equillibrium

Author: Pavlo R. Blavatskyy

Publisher:

Published: 2015

Total Pages: 20

ISBN-13:

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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 a 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. An interpretation of our refinement in terms of the implicit model of relative random errors is provided.