Multilayers in a modulated stochastic game

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:353

Article

Dshalalow, Jewgeni H.¹  Ke, Hao-Jan¹ 

[1] Florida Inst Technol, Dept Math Sci, Coll Sci, Melbourne, FL 32901 USA

关键词: Noncooperative games;    Fluctuation theory;    Marked point processes;    Poisson process;    Ruin time;    Exit time;    First passage time;   

DOI  :  10.1016/j.jmaa.2008.12.026

来源: Elsevier

【 摘 要 】

We are concerned with an antagonistic stochastic game between two players A and B which finds applications in economics and warfare. The actions of the players are manifested by a series of strikes of random magnitudes at random times exerted by each player against his opponent. Each of the assaults inflicts a random damage to enemy's vital areas. In contrast with traditional games, in our setting, each player can endure multiple strikes before perishing. Predicting the ruin time (exit) of player A, along with the total amount of casualties to both players at the exit is a main objective of this work. In contrast to the time sensitive analysis (earlier developed to refine the information on the game) we insert auxiliary control levels, which both players will cross in due game before the ruin of A. This gives A (and also B) an additional opportunity to reevaluate his strategy and change the course of the game. We formalize such a game and also allow the real time information about the game to be randomly delayed. The delayed exit time, cumulative casualties to both players, and prior crossings are all obtained in a closed-form joint functional. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free