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On the stability of CSS under the replicator dynamic

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  • Louge, Fernando

    (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.

Suggested Citation

  • Louge, Fernando, 2011. "On the stability of CSS under the replicator dynamic," Center for Mathematical Economics Working Papers 436, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:436
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    File URL: https://pub.uni-bielefeld.de/download/2316463/2319875
    File Function: First Version, 2010
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    Cited by:

    1. Fernando Louge & Frank Riedel, 2012. "Evolutionary Stability in First Price Auctions," Dynamic Games and Applications, Springer, vol. 2(1), pages 110-128, March.

    More about this item

    Keywords

    Continuously stable strategy (CSS); Evolutionary stability;

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