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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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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DOI: https://doi.org/10.1007/BF01813890