I was studying definitions of Stochastic and Bayesian game and it appears that Stochastic game is a generalized form of Bayesian game. Could anybody please explain the fundamental differences between Stochastic game and Bayesian game and imperfect information and incomplete information games ?
In a Bayesian game, information is incomplete. To cope, players have beliefs about the state of the game. In a sense, each player strategizes as if the game was as he or she believes. So each player operates in his or her own world. And if every player plays a Nash equilibrium in one's own world, that's a Bayesian Nash equilibrium.
In a stochastic game, the information about the current state of the game may indeed be public. At a given time step, the next state is determined by the current state, the strategy profile played at that time step, and some stochastic process (like a Markov chain, for example).
We can have a stochastic Bayesian game where information is incomplete and there is a stochastic switching device like a Markov chain.