Time averages, recurrence and transience in the stochastic replicator dynamics

DOI10.1214/08-AAP577zbMath1172.60321arXiv0908.4467OpenAlexW3100586253MaRDI QIDQ835062

Lorens A. Imhof, Josef Hofbauer

Publication date: 27 August 2009

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0908.4467

zbMATH Keywords

stochastic differential equationLyapunov functionNash equilibriumaveraging principleDirichlet distributionstochastic asymptotic stabilityinvariant distributionexclusion principle

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Population dynamics (general) (92D25) Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70) Evolutionary games (91A22)

Related Items (14)

Dynamics of some stochastic chemostat models with multiplicative noise ⋮ On the robustness of learning in games with stochastically perturbed payoff observations ⋮ Imitation dynamics with payoff shocks ⋮ A stochastic variant of replicator dynamics in zero-sum games and its invariant measures ⋮ Darwinian evolution as Brownian motion on the simplex: a geometric perspective on stochastic replicator dynamics ⋮ Stochastic replicator dynamics: a theoretical analysis and an experimental assessment ⋮ EVOLUTIONARY DYNAMICS IN DISCRETE TIME FOR THE PERTURBED POSITIVE DEFINITE REPLICATOR EQUATION ⋮ Stochastic functional Kolmogorov equations. I: Persistence ⋮ Multiple-trial conflicts and stochastic evolutionary game dynamics ⋮ The emergence of rational behavior in the presence of stochastic perturbations ⋮ Metastability in stochastic replicator dynamics ⋮ A general theory of coexistence and extinction for stochastic ecological communities ⋮ Stochastic functional Kolmogorov equations. II: Extinction ⋮ Long-run analysis of the stochastic replicator dynamics in the presence of random jumps

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