A dynkin game on assets with incomplete information on the return

This paper studies a 2-players zero-sum Dynkin game arising from pricing an option on an asset whose rate of return is unknown to both players. Using filtering techniques we first reduce the problem to a zero-sum Dynkin game on a bi-dimensional diffusion (X, Y ). Then we characterize the existence of a Nash equilibrium in pure strategies in which each player stops at the hitting time of (X, Y ) to a set with moving boundary. A detailed description of the stopping sets for the two players is provided along with global C1 regularity of the value function.