Two-player stochastic games. II: The case of recursive games (Q1594890)

This paper complements Part I [Isr. J. Math. 119, 55-91 (2000; Zbl 0974.91005)]. The author considers zero-sum positive recursive games which are recursive games in which the payoff of one of the players is positive in each absorbing state. Such a game is absorbing if the other player cannot prevent the play from reaching an absorbing state in finite time. He proves that every positive absorbing recursive game has an equilibrium payoff. Two examples are also described. Finally in the last section, he defines a family of constrained games indexed by \(\varepsilon> 0\), and analyzes the asymptotics of the family, as \(\varepsilon\) goes to 0.