Positive Markov games with stopping actions

In this paper we consider the two-person zero-sum Markov (stochastic) game with finite state and action spaces, where the immediate payoffs from player II to player I are strictly positive, but where player II has in each state an action which terminates the play immediately. This game is a special case of the positive Markov games considered by Kushner and Chamberlain. Making explicit use of the fact that player II can terminate the game immediately we derive with the method of successive approximations, an e-band for the value of the game and stationary e-optimal strategies for both players.