Time averages, recurrence and transience in the stochastic replicator dynamics

Hofbauer, Josef; Imhof, Lorens A.

Ann. Appl. Probab., Tome 19 (2009) no. 1, p. 1347-1368 / Harvested from Project Euclid

Résumé

We investigate the long-run behavior of a stochastic replicator process, which describes game dynamics for a symmetric two-player game under aggregate shocks. We establish an averaging principle that relates time averages of the process and Nash equilibria of a suitably modified game. Furthermore, a sufficient condition for transience is given in terms of mixed equilibria and definiteness of the payoff matrix. We also present necessary and sufficient conditions for stochastic stability of pure equilibria.

Publié le : 2009-08-15
Classification: Averaging principle, Dirichlet distribution, exclusion principle, invariant distribution, Lyapunov function, Nash equilibrium, stochastic asymptotic stability, stochastic differential equation, 60H10, 60J70, 91A22, 92D25

@article{1248700620,
     author = {Hofbauer, Josef and Imhof, Lorens A.},
     title = {Time averages, recurrence and transience in the stochastic replicator dynamics},
     journal = {Ann. Appl. Probab.},
     volume = {19},
     number = {1},
     year = {2009},
     pages = { 1347-1368},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1248700620}
}

Hofbauer, Josef; Imhof, Lorens A. Time averages, recurrence and transience in the stochastic replicator dynamics. Ann. Appl. Probab., Tome 19 (2009) no. 1, pp.  1347-1368. http://gdmltest.u-ga.fr/item/1248700620/