New results on a stochastic duel game with each force consisting of heterogeneous units

New results on a stochastic duel game with each force consisting of heterogeneous units

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Article ID: iaor201524008
Volume: 61
Issue: 1
Start Page Number: 56
End Page Number: 65
Publication Date: Feb 2014
Journal: Naval Research Logistics (NRL)
Authors:
Keywords: stochastic processes, military & defence
Abstract:

Two forces engage in a duel, with each force initially consisting of several heterogeneous units. Each unit can be assigned to fire at any opposing unit, but the kill rate depends on the assignment. As the duel proceeds, each force–knowing which units are still alive in real time–decides dynamically how to assign its fire, in order to maximize the probability of wiping out the opposing force before getting wiped out. It has been shown in the literature that an optimal pure strategy exists for this two‐person zero‐sum game, but computing the optimal strategy remained cumbersome because of the game's huge payoff matrix. This article gives an iterative algorithm to compute the optimal strategy without having to enumerate the entire payoff matrix, and offers some insights into the special case, where one force has only one unit.

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