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Evolutionary Selection in Normal-Form Games Author(s): Klaus Ritzberger and Jörgen W. Weibull Source: Econometrica, Vol. 63, No. 6 (Nov., 1995), pp. 1371-1399 Published by: The Econometric Society Stable URL: http://www.jstor.org/stable/2171774 Accessed: 03/06/2010 03:19
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1995),1371-1399 Econometrica, Vol. 63, No. 6 (November,

EVOLUTIONARYSELECTION IN NORMAL-FORM GAMES
BY KLAus RITZBERGERAND JORGEN W. WEIBULL1 This paper investigates stability properties of evolutionaryselection dynamicsin dynamics continuoustime in normal-form games.The analysisis focusedon deterministic and on asymptotic stabilityof sets of populationstates, more preciselyof faces of the of mixed-strategy space. The main result is a characterization those faceswhich are asymptotically stable in all dynamicsfrom a certainclass, and we show that every such face contains an essential component of the set of Nash equilibria, and hence a strategically stable set in the sense of Kohlbergand Mertens(1986). games,stability. KEYWORDS:Dynamics, evolution,noncooperative 1. INTRODUCTION

such solution concepts as Nash equilibrium.As is well known by now, therationalistic foundationof this approachis quite demanding.Not only is it requiredthat agents be optimizers,but it also presumes a large degree of coordinationof differentagents' expectations(see, e.g., Tan and Werlang(1988), and Aumann and Brandenburger (1992)).In recent years researchershave investigatedalterpromisingseems the native foundationsof Nash equilibriumplay. Particularly approachtaken inevolutionarygame theory. Instead of asking if agents are rationalin some epistemologically well-definedsense, one asks if evolutionary selection processes induce a tendency towards aggregate Nash equilibrium behavior.In other words,one then investigatesthe validityof Friedman's (1953) "as if' paradigmin the context of strategicinteraction. The idea of an "as if' interpretationof equilibriumpoints,however,dates back to the early days of Nash equilibrium:
"We shallnow take up the "mass-action" of interpretation equilibrium points. ... It is of to have full knowledgeof the total structure unnecessary assumethat the participants the game, or the abilityand inclinationto go throughany complexreasoningprocesses. But the participants supposedto accumulateempiricalinformationon the relative areof advantages the variouspure strategiesat their disposal. of To be more detailed,we assumethat there is a population the sense of statistics) (in for playing" participants each positionof the game.Let us also assumethat the "average and of the game involvesn participants selected at randomfrom the n populations, that there is a stable averagefrequencywith which each pure strategyis employedby...
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