2018/01/07 by Avrachenkov, Konstantin, Borkar, Vivek S.
#34F05 #60H10 #Computer Science and Game Theory (cs.GT) #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Optimization and Control (math.OC) #Primary: 91A22 #Probability (math.PR) #Secondary: 91A25
paper · doi:10.48550/arxiv.1801.02161
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.