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Hybrid mean field game dynamics in large population

We consider finite populations of interacting players with different types and finite action set per type. Under suitable conditions we derive the mean field game dynamics which can be deterministic or stochastic depending on how the system behave with the time-scales. Connection between mean field game dynamics and evolutionary game dynamics are established. Considering different revision protocols for each player, we derive an hybrid mean field game dynamics which offers the possibility of elimination of non-Nash rest points and give nice convergence properties in potential games and stable games.