Mathematics – Probability
Scientific paper
2009-08-31
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.
Hofbauer Josef
Imhof Lorens A.
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