Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 713642, 14 pages
Research Article

Set-Theoretic Inequalities in Stochastic Noncooperative Games with Coalition

Jewgeni H. Dshalalow and Ailada Treerattrakoon

Department of Mathematical Sciences, College of Science, Florida Institute of Technology, Melbourne, FL 32901, USA

Received 11 November 2007; Accepted 15 January 2008

Academic Editor: Donald O'Regan

Copyright © 2008 Jewgeni H. Dshalalow and Ailada Treerattrakoon. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We model and analyze antagonistic stochastic games of three players, two of whom form a coalition against the third one. The actions of the players are modeled by random walk processes recording the cumulative damages to each player at any moment of time. The game continues until the single player or the coalition is defeated. The defeat of any particular player takes place when the associated process (representing the collateral damage) crosses a fixed threshold. Once the threshold is exceeded at some time, the associated player exits the game. All involved processes are being “observed by a third party process” so that the information regarding the status of all players is restricted to those special epochs. Furthermore, all processed are modulated (with their parameters being modified in due course of the game). We obtain a closed form joint functional of the named processes at key reference points.