  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.
