Research Reports from the Department of Operations
Document Type
Dissertation
Publication Date
8-1-1973
Abstract
Markov decision processes and stochastic games have been considered in this dissertation. An infinite planning horizon is assumed. Both discounted and undiscounted cash flows have been treated. In Markov decision process, a two-dimensional reward structure is considered and the objective criterion is to maximize the rate of return. It has been shown that a pure stationary optimal policy exists, whenever the rewards are finite and, in particular, the investment part of cash flow is positive. In the case of discounted cash flows, the optimal policy depends on the initial state the process is in. Finite algorithms have been proposed to find the optimal policies. The stochastic games are defined with bimatrix payoffs. The criterion used is the ratio of the payoffs to the two players in the discounted case and the ratio of reward rates in the undiscounted case. An optimal policy exists in stationary strategies and a convergent algorithm has been given to find the solution for the games.
Keywords
Stochastic processes, Operations research, Markov processes, Decision making--Mathematical models, Cash flow--Mathematical models, Mathematical optimization, Rate of return, Equilibrium (Economics)
Publication Title
Dissertation/Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University
Issue
Technical memorandum no. 309 ; Submitted in partial fulfillment of the requirements for the Degree of Doctor of Philosophy
Rights
This work is in the public domain and may be freely downloaded for personal or academic use
Recommended Citation
Aggarwal, Vijaykumar V., "Bimatrix Markovian Decision Processes and Stochastic Ratio Games" (1973). Research Reports from the Department of Operations. 58.
https://commons.case.edu/wsom-ops-reports/58