Evolutionary stability in asymmetric games.

*(English)*Zbl 0770.90096The authors consider an evolutionary selection game between two asymmetric players. Consequences of regularity and monotonic evolutions, in the case of strictly dominated strategies, are discussed. Conditions for the existence of replicator dynamic functions in a regular aggregate monotonic process are derived. A comparison of asymptotic stability and of a strict Nash equilibrium is presented. Evolutionary models with births and mutations are also discussed. Stable evolutions are proven not to need to respect weak dominance.

Reviewer: L.F.Pau (Valbonne)

##### Keywords:

evolutionary selection game; asymmetric playes; strictly dominated strategies; asymptotic stability; strict Nash equilibrium
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\textit{L. Samuelson} and \textit{J. Zhang}, J. Econ. Theory 57, No. 2, 363--391 (1992; Zbl 0770.90096)

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