On the asymptotic convergence to mixed equilibria in 2×2 asymmetric games (original) (raw)

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 the_Modified 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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Authors and Affiliations

1. Universitat Pompeu Fabra, Ramon Trias Fargas 25-27, 08005, Barcelona, Spain
   María Sáez-Martí

Additional information

I thank Ken Binmore, Tilman Borgers, Esther Hauk, Sjaak Hurkens, Andreu Mas Colell, Hyun Song Shin, Jörgen Weibull, Fabrizio Zilibotti, an anonymous referee and an associate editor for helpful comments. Financial support from the Bank of Spain is gratefully acknowledged.

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Sáez-Martí, M. On the asymptotic convergence to mixed equilibria in 2×2 asymmetric games.Int J Game Theory 26, 549–559 (1997). https://doi.org/10.1007/BF01813890

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• Received: 15 February 1996
• Revised: 15 November 1996
• Accepted: 15 January 1997
• Issue date: December 1997
• DOI: https://doi.org/10.1007/BF01813890

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