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Metastability in Stochastic Replicator Dynamics

Abstract : We consider a novel model of stochastic replicator dynamics for potential games that converts to a Langevin equation on a sphere after a change of variables. This is distinct from the models of stochastic replicator dynamics studied earlier. In particular, it is ill-posed due to non-uniqueness of solutions, but is amenable to a natural selection principle that picks a unique solution. The model allows us to make specific statements regarding metastable states such as small noise asymptotics for mean exit times from their domain of attraction, and quasi-stationary measures. We illustrate the general results by specializing them to replicator dynamics on graphs and demonstrate that the numerical experiments support theoretical predictions.
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Submitted on : Saturday, December 7, 2019 - 4:56:39 PM
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Konstantin Avrachenkov, Vivek Borkar. Metastability in Stochastic Replicator Dynamics. Dynamic Games and Applications, Springer Verlag, 2019, 9 (2), pp.366-390. ⟨10.1007/s13235-018-0265-7⟩. ⟨hal-02398561⟩



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