Time averages, recurrence and transience in the stochastic replicator dynamics

Details Time averages, recurrence and transience in the stochastic replicator dynamics Time averages, recurrence and transience in the stochastic replicator dynamics

2009-08-31

arxiv.org/abs/0908.4467v1

Annals of Applied Probability 2009, Vol. 19, No. 4, 1347-1368

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/08-AAP577 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/08-AAP577

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.

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