On the stability of CSS under the replicator dynamic

Fernando Louge
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Fernando Louge: Center for Mathematical Economics, Bielefeld University

No 436, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: This paper considers a two-player game with a one-dimensional continuous strategy. We study the asymptotic stability of equilibria under the replicator dynamic when the support of the initial population is an interval. We find that, under strategic complementarities, Continuously Stable Strategy (CSS) have the desired convergence properties using an iterated dominance argument. For general games, however, CSS can be unstable even for populations that have a continuous support. We present a sufficient condition for convergence based on elimination of iteratively dominated strategies. This condition is more restrictive than CSS in general but equivalent in the case of strategic complementarities. Finally, we offer several economic applications of our results.

Keywords: Continuously stable strategy (CSS); Evolutionary stability (search for similar items in EconPapers)
Date: 2011-08-16
New Economics Papers: this item is included in nep-evo and nep-gth
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Citations: View citations in EconPapers (1)

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https://pub.uni-bielefeld.de/download/2316463/2319875 First Version, 2010 (application/pdf)

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Persistent link: https://EconPapers.repec.org/RePEc:bie:wpaper:436

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