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On the stability of CSS under the replicator dynamic

  • Louge, Fernando

    (Center for Mathematical Economics, Bielefeld University)

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    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.

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    File URL: https://pub.uni-bielefeld.de/download/2316463/2319875
    File Function: First Version, 2010
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    Paper provided by Center for Mathematical Economics, Bielefeld University in its series Center for Mathematical Economics Working Papers with number 436.

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    Date of creation: 16 Aug 2011
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    Handle: RePEc:bie:wpaper:436
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