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On Terminating Stochastic Games

Author

Listed:
  • H. Mine

    (Kyoto University, Kyoto, Japan)

  • K. Yamada

    (Kyoto University, Kyoto, Japan)

  • S. Osaki

    (Kyoto University, Kyoto, Japan)

Abstract

This paper describes a stochastic game in which the play terminates in a finite number of steps with probability 1. The game is called a terminating stochastic game. When the play terminates at any step, the play is regarded to reach to an absorbing state in the Markov chain under consideration. Hence, the terminating stochastic game is a nonstationary Markov chain with rewards in which our concern is the transient behavior before absorption. In particular, when one of the players is a dummy, the stochastic game reduces to a Markovian decision process of special type. This paper discusses such games. We introduce a new concept of rewards and formulate three problems arising in the games by linear programming. Finally, numerical examples are presented.

Suggested Citation

  • H. Mine & K. Yamada & S. Osaki, 1970. "On Terminating Stochastic Games," Management Science, INFORMS, vol. 16(9), pages 560-571, May.
    • Handle: RePEc:inm:ormnsc:v:16:y:1970:i:9:p:560-571
    DOI: 10.1287/mnsc.16.9.560
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    Cited by:

    1. Rogiers, J. & Tachiki, M., 1977. "Spin ordering in spin-pair systems: The XY model in an external field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 87(3), pages 614-622.

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