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This paper studies a 2-players zero-sum Dynkin game arising from pricing anoption on an asset whose rate of return is unknown to both players. Usingfiltering techniques we first reduce the problem to a zero-sum Dynkin game on abi-dimensional diffusion $(X,Y)$. Then we characterize the existence of a Nashequilibrium in pure strategies in which each player stops at the hitting timeof $(X,Y)$ to a set with moving boundary. A detailed description of thestopping sets for the two players is provided along with global $C^1$regularity of the value function.

A Dynkin game on assets with incomplete information on the return