Stochastic games with a single controller and incomplete information

We study stochastic games with incomplete information on one side, where the transition is controlled by one of the players. We prove that if the informed player also controls the transition, the game has a value, whereas if the uninformed player controls the transition, the max-min value, as well as the min-max value, exist, but they may differ. We discuss extensions to the case of incomplete information on both sides