Metastability in Stochastic Replicator Dynamics

Konstantin Avrachenkov; Vivek S. Borkar

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arXiv · 1801.02161

Metastability in Stochastic Replicator Dynamics

Konstantin Avrachenkov·Vivek S. Borkar

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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 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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BibTeX RIS

Konstantin Avrachenkov, Vivek S. Borkar. 2018-01-07. Metastability in Stochastic Replicator Dynamics. https://arxiv.org/abs/1801.02161

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