Time averages, recurrence and transience in the stochastic replicator dynamics
نویسندگان
چکیده
منابع مشابه
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 tran-sience is given in terms of mixed equilibria and definiteness of t...
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We have the following dichotomy result. Theorem 2. The following are equivalent: (1) X is transient; (2) X is not recurrent; (3) U0(B(0 � �)) < ∞ for all � > 0. Theorem 2 has the following important dichotomous implication: Either X is transient, or X is recurrent [and not both]. The proof relies on a convenient series of equivalences. Proposition 3. The following are equivalent: (1) sup�∈R� U0...
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ژورنال
عنوان ژورنال: The Annals of Applied Probability
سال: 2009
ISSN: 1050-5164
DOI: 10.1214/08-aap577