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August 2009 Time averages, recurrence and transience in the stochastic replicator dynamics
Josef Hofbauer, Lorens A. Imhof
Ann. Appl. Probab. 19(4): 1347-1368 (August 2009). DOI: 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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Josef Hofbauer. Lorens A. Imhof. "Time averages, recurrence and transience in the stochastic replicator dynamics." Ann. Appl. Probab. 19 (4) 1347 - 1368, August 2009.


Published: August 2009
First available in Project Euclid: 27 July 2009

zbMATH: 1172.60321
MathSciNet: MR2538073
Digital Object Identifier: 10.1214/08-AAP577

Primary: 60H10 , 60J70 , 91A22 , 92D25

Keywords: averaging principle , Dirichlet distribution , exclusion principle , Invariant distribution , Lyapunov function , Nash equilibrium , stochastic asymptotic stability , Stochastic differential equation

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.19 • No. 4 • August 2009
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