A decomposition approach for undiscounted two-person zero-sum stochastic games

Date

1999-06-01

Author

Avşar, Zeynep Müge

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Two-person zero-sum stochastic games are considered under the long-run average expected payoff criterion. State and action spaces are assumed finite. By making use of the concept of maximal communicating classes, the following decomposition algorithm is introduced for solving two-person zero-sum stochastic games: First, the state space is decomposed into maximal communicating classes. Then, these classes are organized in an hierarchical order where each level may contain more than one maximal communicating class. Best stationary strategies for the states in a maximal communicating class at a level are determined by using the best stationary strategies of the states in the previous levels that are accessible from that class. At the initial level, a restricted game is defined for each closed maximal communicating class and these restricted games are solved independently. It is shown that the proposed decomposition algorithm is exact in the sense that the solution obtained from the decomposition procedure gives the best stationary strategies for the original stochastic game.

Subject Keywords

Management Science and Operations Research, Software, General Mathematics

URI

https://hdl.handle.net/11511/35218

Journal

MATHEMATICAL METHODS OF OPERATIONS RESEARCH

DOI

https://doi.org/10.1007/s001860050063

Collections

Department of Industrial Engineering, Article

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Citation Formats

Z. M. Avşar, “A decomposition approach for undiscounted two-person zero-sum stochastic games,” MATHEMATICAL METHODS OF OPERATIONS RESEARCH, pp. 483–500, 1999, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/35218.