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 ?
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$\begingroup$ This may also be relevant: stochastic Bayesian games combine stochastic games with Bayesian games, see Wikipedia: en.wikipedia.org/wiki/Bayesian_game#Stochastic_Bayesian_games $\endgroup$– AnonymousCommented Apr 12, 2022 at 12:31
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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.
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$\begingroup$ you mentioned that the next state depends upon some stochastic process as well. Do that mean that its "like Markov chain" or is indeed exactly markov chain. In other words the next stage could be one of 4 states with probability attached to each of the 4 states? In Bayesian game, isnt this also the case? Does Bayesian game dont have transition probability? $\endgroup$– user0193Commented Jan 1, 2022 at 10:19