Multilayers in a modulated stochastic game

Abstract

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.

Current Trends in Random Walks on Random Lattices

“…The model is definitely not a stochastic game in the traditional sense, but it serves purposes of a game-related setting and as such it works very well to model wars, economic competitions, and stock and stock option trading, to name a few. Dshalalow [56,57], Dshalalow and Liew [58][59][60] studied applications of random walk fluctuations to finance, while Dshalalow and Huang [53][54][55], Dshalalow and Iwezulu [61], Dshalalow and Ke [62,63], and Dshalalow and Treerattrakoon [64] studied exclusively antagonistic games and in the latter case, with three players two of whom can team up against the third player. Dshalalow and White [65,66] focused on random walks applications to stochastic networks.…”

“…Note that since the escape of random walks offer predictive tools for outcomes of the games such as those occurring in finance, it stands for reason to refine the information that leads to ruin. One of such efforts were undertaken in Dshalalow and Ke [62,63] by introducing a smaller subset A ⊆ A that a walk will escape from before it escapes from A that should give us an extra layer of security. Another way to refine the information is to allow an access to the underlying walk at any epoch of time, thereby making it time dependent.…”

Time sensitive analysis of independent and stationary increment processes

“…The time-sensitive tools can be utilized in other time-insensitive models, in particular in stochastic games, queueing, and finance [5,6]. In some earlier forms, time-sensitive analysis was known in queueing [2] (under the name of semi-regenerative techniques) and in other stochastic processes such as Cox [1] to interpolate stationary probabilities of embedded processes.…”

On Strategic Defense in Stochastic Networks

“…The information associated with the M 1 -threshold will become more conclusive on what leads to critical threshold crossings of the network. The idea of an auxiliary threshold stems from Dshalalow and Ke [8] applied there to stochastic games, with different utility and development compared to the present paper.…”