Large deviations and Stochastic stability in Population Games

In this article we review a model of stochastic evolution under general noisy best-response protocols, allowing the probabilities suboptimal choices to depend on their payoff consequences. We survey methods developed by authors which allow for quantitative analysis these evolutionary game dynamics. start with compact techniques designed study long run behavior in small noise double limit (SNDL). In regime let level agents' decision rules approach zero, and then population size is formally taken infinity. This iterated strategy yields family deterministic optimal control problems admit an explicit many instances. move describing main steps analyze dynamics large (LPDL). refers first infinity decisions vanishes. The mathematical LPDL relies sample-path deviations principle Markov chains polyhedra. setting formulate set conjectures open give clear direction future research activities.