A Hybrid Di erential Stochastic Zero Sum Game with Fast Stochastic Part

We consider in this paper a continuous time stochastic hybrid sys tem with a nite time horizon controlled by two players with opposite objectives zero sum game Player one wishes to maximize some linear function of the expected state trajectory and player two wishes to mini mize it The state evolves according to a linear dynamics The parameters of the state evolution equation may change at discrete times according to a MDP i e a Markov chain that is directly controlled by both players and has a countable state space Each player has a nite action space We use a procedure similar in form to the maximum principle this determines a pair of stationary strategies for the players which is asymptotically a saddle point as the number of transitions during the nite time horizon grows to in nity