1. OPTIMAL STOPPING IN SEQUENTIAL GAMES WITH OR WITHOUT A CONSTRAINT OF ALWAYS TERMINATING.
- Author
-
Ohtsubo, Yoshio
- Subjects
GAME theory ,MATHEMATICAL models ,PROBLEM solving ,ALGORITHMS ,MARKOV processes ,STOCHASTIC processes ,OPERATIONS research ,DECISION making ,MATHEMATICS - Abstract
Zero-sum sequential games where both control variables are stopping times are considered. Two game problems are dealt with: (G[sub 1]) is a problem in which the players are allowed the possibility of not stopping the game, and in the other (G[sub 2]) they are obliged to stop the observed process at some finite (but not preassigned) time. The problem (G[sub 1]) is well known. In the present paper we mainly investigate (G[sub 2]) as compared with (G[sub 1]). We give sufficient conditions for the game problem (G[sub 2]) to have a value which is consequently equal to that of (G[sub 1]) and, in parallel with it, present the constructive algorithm of the value in the natural form. The saddle point in each problem is found under a certain condition. The monotone case and the Markov case are finally investigated as the special cases. [ABSTRACT FROM AUTHOR]
- Published
- 1986
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