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Evolutionary dynamics on infinite strategy spaces

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  • JÃrg Oechssler

    ()
    (Department of Economics, University of Bonn, Adenauerallee 24, 53113 Bonn, GERMANY)

  • Frank Riedel

    ()
    (Department of Economics, Humboldt University, Spandauer Strañe 1, 10178 Berlin, GERMANY)

Abstract

The study of evolutionary dynamics was so far mainly restricted to finite strategy spaces. In this paper we show that this unsatisfying restriction is unnecessary. We specify a simple condition under which the continuous time replicator dynamics are well defined for the case of infinite strategy spaces. Furthermore, we provide new conditions for the stability of rest points and show that even strict equilibria may be unstable. Finally, we apply this general theory to a number of applications like the Nash demand game, the War of Attrition, linear-quadratic games, the harvest preemption game, and games with mixed strategies.

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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 17 (2001)
Issue (Month): 1 ()
Pages: 141-162

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Handle: RePEc:spr:joecth:v:17:y:2001:i:1:p:141-162

Note: Received: June 25, 1999; revised version: January 31, 2000
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Related research

Keywords: Replicator dynamics; Evolutionary stability; Continuous strategy spaces.;

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  1. J. Hofbauer & P. Schuster & K. Sigmund, 2010. "A Note on Evolutionary Stable Strategies and Game Dynamics," Levine's Working Paper Archive 441, David K. Levine.
  2. Steffen Huck & Georg Kirchsteiger & Jörg Oechssler, 2005. "Learning to like what you have - explaining the endowment effect," Economic Journal, Royal Economic Society, vol. 115(505), pages 689-702, 07.
  3. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, December.
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