Metastability in Stochastic Replicator Dynamics

Konstantin Avrachenkov (1) , Vivek Borkar (2)

1 NEO - Network Engineering and Operations
2 EE-IIT - Department of Electrical Engineering [IIT-Bombay]

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.

Mots clés: stochastic replicator dynamics; Langevin equation on sphere; metastable states; intermittency; small noise asymptotics; mean exit time; quasi-stationary distributions

Domaines: Probabilités [math.PR]; Bio-Informatique, Biologie Systémique [q-bio.QM]; Informatique [cs]

Konstantin Avrachenkov, Vivek Borkar. Metastability in Stochastic Replicator Dynamics. Dynamic Games and Applications, 2019, 9 (2), pp.366-390. ⟨10.1007/s13235-018-0265-7⟩. ⟨hal-02398561⟩