Stationary strategies for recursive games

We study two-person, zero-sum recursive matrix games framing them in the more general context of nonleavable games. Our aim is to extend a result of Orkin by proving that a uniformly epsilon-optimal stationary strategy is available to player I (player II) in any recursive game such that the set where the value of the game is strictly greater (less) than its utility is finite. The proof exploits some new connections between nonleavable and leavable games. In particular we find sufficient conditions for the existence of epsilon-optimal stationary strategies for player I in a leavable game and we use these as a basis for constructing uniformly epsilon-optimal stationary strategies for the recursive games with which we are concerned.