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On the asymptotic convergence to mixed equilibria in 2×2 asymmetric games


Sáez-Martí, María (1997). On the asymptotic convergence to mixed equilibria in 2×2 asymmetric games. International Journal of Game Theory, 26(4):549-559.

Abstract

We analyse the stability properties of mixed equilibria in 2×2 asymmetric games under evolutionary dynamics. With the standard replicator dynamics these equilibria are stable but not asymptotically stable. We modified the replicator dynamics by introducing players of two types: myopies — like in the standard replicator dynamics — and best
responders. The behaviour of the latter is described by a continuos time version of the best reply dynamics. Asymptotic convergence under theModified Replicator Dynamics is proved by identifying a strictly decreasing Ljapunov function. We argue that the finding has important implications to justify the use of economic models with mixed strategy equilibria.

Abstract

We analyse the stability properties of mixed equilibria in 2×2 asymmetric games under evolutionary dynamics. With the standard replicator dynamics these equilibria are stable but not asymptotically stable. We modified the replicator dynamics by introducing players of two types: myopies — like in the standard replicator dynamics — and best
responders. The behaviour of the latter is described by a continuos time version of the best reply dynamics. Asymptotic convergence under theModified Replicator Dynamics is proved by identifying a strictly decreasing Ljapunov function. We argue that the finding has important implications to justify the use of economic models with mixed strategy equilibria.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Economics
Dewey Decimal Classification:330 Economics
Uncontrolled Keywords:Game Theory, Economics, Social and Behavior, Sciences, Economic Theory, Operation Research/Decision Theory, Organization/Planning
Language:English
Date:December 1997
Deposited On:20 May 2015 12:31
Last Modified:05 Apr 2016 19:15
Publisher:Springer
ISSN:0020-7276
Publisher DOI:https://doi.org/10.1007/BF01813890

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