Set-Theoretic Inequalities in Stochastic Noncooperative Games with Coalition

Jewgeni H Dshalalow,Ailada Treerattrakoon

doi:10.1155/2008/713642

Jewgeni H Dshalalow, Ailada Treerattrakoon

Open Access

https://doi.org/10.1155/2008/713642

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Abstract

Wemodel 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.

Highlights

Antagonistic games are those with two players A and B having totally opposite interests
The game ends if player C is defeated by A or B
One of them, say A, can be defeated by player C followed by the defeat of player C by player B

Summary

Introduction

Antagonistic games are those with two players A and B having totally opposite interests. The Poisson processes of 1.1 are conditionally independent in each interval τj−1, τj given the status of the players at τj−1 and, their respective parameters i.e., intensities of marks will depend on the game status at τj−1. This makes perfect sense because if one of the players, say A, is defeated at some point known at τk, his upcoming actions against player C can be reduced or completely halted. Article 3 is somewhat related to our present paper, as it models a noncooperative game by random walk processes, but with two active players only. We mention a few related papers 8, 16–21 which all use different techniques and settings

Preliminaries

Main results