Research Articles

Economic Theory

, Volume 17, Issue 1, pp 141-162

First online:

Evolutionary dynamics on infinite strategy spaces

  • Jörg OechsslerAffiliated withDepartment of Economics, University of Bonn, Adenauerallee 24, 53113 Bonn, GERMANY (e-mail:
  • , Frank RiedelAffiliated withDepartment of Economics, Humboldt University, Spandauer Straße 1, 10178 Berlin, GERMANY (e-mail:

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Summary. 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.

Keywords and Phrases:Replicator dynamics, Evolutionary stability, Continuous strategy spaces.
JEL Classification Numbers:C70, C72.