Stochastic Games with Lack of Information on One Side and Positive Stop Probabilities

We examine Stochastic Games with Lack of Information on One Side (SGLIOS) under the assumption that at each state the game ends with positive probability. The existence of a myopic, stationary in some sense, optimal strategy for the informed player is established. The main tool to approach the problem of control under incomplete information is an updating mechanism using posterior probabilities on the state space given the history up to the present stage.