The long-run behavior of the stochastic replicator dynamics

Details The long-run behavior of the stochastic replicator dynamics The long-run behavior of the stochastic replicator dynamics

2005-03-24

arxiv.org/abs/math/0503529v1

Annals of Applied Probability 2005, Vol. 15, No. 1B, 1019-1045

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051604000000837 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051604000000837

Fudenberg and Harris' stochastic version of the classical replicator dynamics is considered. The behavior of this diffusion process in the presence of an evolutionarily stable strategy is investigated. Moreover, extinction of dominated strategies and stochastic stability of strict Nash equilibria are studied. The general results are illustrated in connection with a discrete war of attrition. A persistence result for the maximum effort strategy is obtained and an explicit expression for the evolutionarily stable strategy is derived.

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