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arXiv · 0908.4467

Time averages, recurrence and transience in the stochastic replicator dynamics

Josef Hofbauer·Lorens A. Imhof
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Abstract

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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Josef Hofbauer, Lorens A. Imhof. 2009-08-31. Time averages, recurrence and transience in the stochastic replicator dynamics. https://doi.org/10.1214/08-aap577

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