Research Reports from the Department of Operations
Document Type
Report
Publication Date
10-1-1970
Abstract
This paper examines a two-person zero-sum stochastic game with a finite number of states and non-terminating transitions. Unlike prior studies that focus on Markovian reward structures, this work explores semi-Markovian reward structures, deriving the equations that the game's value must satisfy. The study develops convergent algorithms for finite and infinite transitions, considering scenarios with and without discounting. Potential extensions include nonzero-sum games and time-horizon analyses. The model serves as a generalization of Jewell's semi-Markovian decision process in a game-theoretic context and extends the non-terminating stochastic game framework of Hoffman and Karp. This research broadens the scope of stochastic games by incorporating semi-Markovian dynamics and provides a foundation for further theoretical and applied advancements.
Keywords
Stochastic processes, Operations research, Game theory, Markov processes
Publication Title
Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University
Issue
Technical memorandum no. 203
Rights
This work is in the public domain and may be freely downloaded for personal or academic use
Recommended Citation
Chandrasekaran, R.; Nair, K.P. K.; and Subba Rao, S., "Stochastic Games with Semi-Markovian Rewards" (1970). Research Reports from the Department of Operations. 555.
https://commons.case.edu/wsom-ops-reports/555