Uniform value in recursive games.
A recursive game is a stochastic game where the state space is partitioned into two sets, the set \(S\) of nonabsorbing states and the set \(T\) of absorbing states. As long as the game is played in a state of \(S,\) the payoff is \(0\) whatever the players do. Once the game reaches a state in \(T,\) the game remains in a state of the set \(T\) whatever move the players make. In this paper the authors consider a two player recursive game. Suppose \(v_n\) denotes the average payoff of the first n stags. A stochastic game is said to have a uniform value if \(\lim _{n\rightarrow \infty}v_n \) exists. It is known that a uniform value exits if the action and state spaces are finite. In this paper the authors study the conditions under which a recursive game will have a uniform value.
scientific article; zbMATH DE number 1906156