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

Date

1999-06-01

Author

Avşar, Zeynep Müge

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

154
views

0
downloads

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

Suggestions

OpenMETU
Core

A decomposition approach for undiscounted two-person zero-sum stochastic games Baykal-gürsoy, Melike; Avşar, Zeynep Müge (null; 1999-12-07) 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 ...
A metamodeling methodology involving both qualitative and quantitative input factors Tunali, S; Batmaz, I (Elsevier BV, 2003-10-16) This paper suggests a methodology for developing a simulation metamodel involving both quantitative and qualitative factors. The methodology mainly deals with various strategic issues involved in metamodel estimation, analysis, comparison, and validation. To illustrate how to apply the methodology, a regression metamodel is developed for a client-server computer system. In particular, we studied how the response time is affected by the quantum interval, the buffer size. and the total number of terminals whe...
Mutual relevance of investor sentiment and finance by modeling coupled stochastic systems with MARS Kalayci, Betul; Ozmen, Ayse; Weber, Gerhard Wilhelm (Springer Science and Business Media LLC, 2020-08-01) Stochastic differential equations (SDEs) rapidly become one of the most well-known formats in which to express such diverse mathematical models under uncertainty such as financial models, neural systems, behavioral and neural responses, human reactions and behaviors. They belong to the main methods to describe randomness of a dynamical model today. In a financial system, different kinds of SDEs have been elaborated to model various financial assets. On the other hand, economists have conducted research on s...
Stochastic differential games for optimal investment problems in a Markov regime-switching jump-diffusion market Savku, E.; Weber, Gerhard Wilhelm (Springer Science and Business Media LLC, 2020-08-01) We apply dynamic programming principle to discuss two optimal investment problems by using zero-sum and nonzero-sum stochastic game approaches in a continuous-time Markov regime-switching environment within the frame work of behavioral finance. We represent different states of an economy and, consequently, investors' floating levels of psychological reactions by aD-state Markov chain. The first application is a zero-sum game between an investor and the market, and the second one formulates a nonzero-sum sto...
The interval Shapley value: an axiomatization Gok, S. Z. Alparslan; Branzei, R.; Tijs, S. (Springer Science and Business Media LLC, 2010-06-01) The Shapley value, one of the most widespread concepts in operations Research applications of cooperative game theory, was defined and axiomatically characterized in different game-theoretic models. Recently much research work has been done in order to extend OR models and methods, in particular cooperative game theory, for situations with interval data. This paper focuses on the Shapley value for cooperative games where the set of players is finite and the coalition values are compact intervals of real num...

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.