Journal
ANNALS OF APPLIED PROBABILITY
Volume 19, Issue 4, Pages 1347-1368Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/08-AAP577
Keywords
Averaging principle; Dirichlet distribution; exclusion principle; invariant distribution; Lyapunov function; Nash equilibrium; stochastic asymptotic stability; stochastic differential equation
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Funding
- Economic and Social Research Council [RES-538-28-1001] Funding Source: researchfish
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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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