Metastability in Stochastic Replicator Dynamics

Konstantin Avrachenkov () and Vivek S. Borkar ()
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Konstantin Avrachenkov: INRIA Sophia Antipolis
Vivek S. Borkar: Indian Institute of Technology Bombay

Dynamic Games and Applications, 2019, vol. 9, issue 2, No 3, 366-390

Abstract: 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.

Keywords: Stochastic replicator dynamics; Langevin equation on sphere; Metastable states; Intermittency; Small noise asymptotics; Mean exit time; Quasi-stationary distributions; Primary: 91A22; Secondary: 91A25; 60H10; 34F05 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s13235-018-0265-7

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