| Abstract: | Appealing to the theory of stochastic games, a two-person, zero-sum first passage game, which may be viewed as a generalization of the first passage decision problem, is developed. In the first passage game, the players have stationary optional strategies and the values are unique and these can be computed using an algorithm for terminating stochastic games. It is also shown that the solution of a recurrence game is closely related to that of the first passage game. Finally, it is shown that a finite step stochastic game with nonstationary transition probabilities and payoffs can be converted to a first passage game whose solution yields a solution of the original finite step game. The first passage game so obtained has stationary transition probabilities and payoffs. Because of its special structure, the solution method reduces to a dynamic programming recursion in the context of games. |
