Since the pathbreaking paper Stochastic Games (1953) by Shapley, people have analyzed stochastic games and their deterministic counterpart, dynamic games, by examining Markov Perfect Equilibria, equilibria that condition only on the state and are sub-game perfect. Now these games are essentially all games with observable actions. I would like to know if there are analog equilibrium concepts for games with persistent incomplete information. With persistent, I mean that private information is not independent between periods, so that players have to actually learn.
Motivation: I have written a paper on a certain conceptual issue of Markov Perfect Equilibrium (the definition of the state space). Several applied economists have asked me if a similar analysis can be done for MPE in incomplete information games. So I would like to know how the notion is applied in the literature.