Stopping games for continuous time Markov chains with incomplete information

Résumé

We study a model of a two-player, zero-sum, stopping game with incomplete information on both sides. We assume that the payoff depends on two continuous-time Markov chains (X_t),(Y_t) where (X_t) is only observed by player 1 and (Y_t) only by player 2. We show the existence of a value by PDE methods. In the case of incomplete information on one side we establish a different characterisation of the value by a stochastic optimisation problem and study an example in case of a two state Markov process. (Joint work with F. Gensbittel)