Stochastic Games with Semi-Markovian Rewards.
CASE WESTERN RESERVE UNIV CLEVELAND OHIO DEPT OF OPERATIONS RESEARCH
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The paper discusses a two-person zero sum stochastic game with finite number of positions or states. The movement of the game from state to state is jointly controlled by the players depending on their choices of strategies from a finite number of alternatives in each state available to each of them. Since no stop probability is introduced, the game is of non-terminating type. Available literature on this type of game is limited to those with Markovian reward structure. In the present work, semi-Markovian reward structure is considered and the equations that the value must satisfy are obtained. Convergent algorithms for the cases of finite and infinite transitions, with and without discounting in each case are presented. Possible extensions to consider time horizon and nonzero-sum situations are indicated. The present work could be considered as a generalization of semi-Markovian decision process developed by Jewell to game theoretic context. Also, the present model generalizes the non-terminating stochastic game of Hoffman and Karp to semi-Markovian reward structure. Author
- Operations Research