Finite Population Dynamics and Mixed Equilibria

Carlos Alós-Ferrer

doi:10.1142/S0219198903001057

Finite Population Dynamics and Mixed Equilibria

Carlos Alós-Ferrer

Economics

Research output: Contribution to journal › Article › peer-review

Abstract

This paper examines the stability of mixed-strategy Nash equilibria of symmetric games, viewed as population profiles in dynamical systems with learning within a single, finite population. Alternative models of imitation and myopic best reply are considered under different assumptions on the speed of adjustment. It is found that two specific refinements of mixed Nash equilibria identify focal rest points of these dynamics in general games. The relationship between both concepts is studied. In the 2 × 2 case, both imitation and myopic best reply yield strong stability results for the same type of mixed Nash equilibria.

Original language	English (US)
Pages (from-to)	263-290
Number of pages	28
Journal	International Game Theory Review
Volume	5
Issue number	3
DOIs	https://doi.org/10.1142/S0219198903001057
State	Published - Sep 2003

Keywords

Best reply dynamics
Imitation dynamics
Learning
Mixed-strategy Nash equilibrium

ASJC Scopus subject areas

Business and International Management
General Computer Science
Statistics, Probability and Uncertainty

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10.1142/S0219198903001057

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title = "Finite Population Dynamics and Mixed Equilibria",

abstract = "This paper examines the stability of mixed-strategy Nash equilibria of symmetric games, viewed as population profiles in dynamical systems with learning within a single, finite population. Alternative models of imitation and myopic best reply are considered under different assumptions on the speed of adjustment. It is found that two specific refinements of mixed Nash equilibria identify focal rest points of these dynamics in general games. The relationship between both concepts is studied. In the 2 × 2 case, both imitation and myopic best reply yield strong stability results for the same type of mixed Nash equilibria.",

keywords = "Best reply dynamics, Imitation dynamics, Learning, Mixed-strategy Nash equilibrium",

author = "Carlos Al{\'o}s-Ferrer",

note = "Funding Information: The author thanks Josef Hofbauer for helpful comments and for providing Example 4.2. Financial support from the European Science Foundation and the Austrian FWF through Project P15281 is gratefully acknowledged.",

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N1 - Funding Information: The author thanks Josef Hofbauer for helpful comments and for providing Example 4.2. Financial support from the European Science Foundation and the Austrian FWF through Project P15281 is gratefully acknowledged.

PY - 2003/9

Y1 - 2003/9

N2 - This paper examines the stability of mixed-strategy Nash equilibria of symmetric games, viewed as population profiles in dynamical systems with learning within a single, finite population. Alternative models of imitation and myopic best reply are considered under different assumptions on the speed of adjustment. It is found that two specific refinements of mixed Nash equilibria identify focal rest points of these dynamics in general games. The relationship between both concepts is studied. In the 2 × 2 case, both imitation and myopic best reply yield strong stability results for the same type of mixed Nash equilibria.

AB - This paper examines the stability of mixed-strategy Nash equilibria of symmetric games, viewed as population profiles in dynamical systems with learning within a single, finite population. Alternative models of imitation and myopic best reply are considered under different assumptions on the speed of adjustment. It is found that two specific refinements of mixed Nash equilibria identify focal rest points of these dynamics in general games. The relationship between both concepts is studied. In the 2 × 2 case, both imitation and myopic best reply yield strong stability results for the same type of mixed Nash equilibria.

KW - Best reply dynamics

KW - Imitation dynamics

KW - Learning

KW - Mixed-strategy Nash equilibrium

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Finite Population Dynamics and Mixed Equilibria

Abstract

Keywords

ASJC Scopus subject areas

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