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.
Complete list of metadatas

Cited literature [67 references]  Display  Hide  Download

https://hal.inria.fr/hal-02398561
Contributor : Konstantin Avrachenkov <>
Submitted on : Saturday, December 7, 2019 - 4:56:39 PM
Last modification on : Tuesday, December 17, 2019 - 2:06:24 AM

File

CurrentVersionForArxiv1.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

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⟩

Share

Metrics

Record views

16

Files downloads

57