Subgame-Perfection in Stochastic Games with Perfect Information and Recursive Payoffs

We consider a class of n-player stochastic games with the following properties: (1) in every state, the transitions are controlled by one player, (2) the payoffs are equal to zero in every non-absorbing state, (3) the payoffs are non-negative in every absorbing state. With respect to the expected average reward, we provide a constructive proof that a subgame-perfect ε -equilibrium exists in pure strategies, for every ε > 0. More-over, if all transitions of a game in our class are deterministic, then the game has a subgame-perfect 0-equilibrium in pure strategies.