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.
Publié le : 2005-02-14
Classification:
Asymptotic stochastic stability,
evolutionarily stable strategy,
invariant measure,
Lyapunov function,
Nash equilibrium,
recurrence,
stochastic differential equation,
war of attrition,
60H10,
60J70,
92D15,
92D25
@article{1107271677,
author = {Imhof, Lorens A.},
title = {The long-run behavior of the stochastic replicator dynamics},
journal = {Ann. Appl. Probab.},
volume = {15},
number = {1A},
year = {2005},
pages = { 1019-1045},
language = {en},
url = {http://dml.mathdoc.fr/item/1107271677}
}
Imhof, Lorens A. The long-run behavior of the stochastic replicator dynamics. Ann. Appl. Probab., Tome 15 (2005) no. 1A, pp. 1019-1045. http://gdmltest.u-ga.fr/item/1107271677/