The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 19, Number 4 (2009), 1347-1368.
Time averages, recurrence and transience in the stochastic replicator dynamics
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.
Ann. Appl. Probab. Volume 19, Number 4 (2009), 1347-1368.
First available in Project Euclid: 27 July 2009
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx] 91A22: Evolutionary games 92D25: Population dynamics (general)
Hofbauer, Josef; Imhof, Lorens A. Time averages, recurrence and transience in the stochastic replicator dynamics. Ann. Appl. Probab. 19 (2009), no. 4, 1347--1368. doi:10.1214/08-AAP577. https://projecteuclid.org/euclid.aoap/1248700620