Accession Number : AD0622049

Title :   A GAME OVER SPACES OF PROBABILITY DISTRIBUTIONS,

Corporate Author : CENTER FOR NAVAL ANALYSES CAMBRIDGE MASS INST OF NAVAL STUDIES

Personal Author(s) : Danskin,John M.

Report Date : 1964

Pagination or Media Count : 34

Abstract : This paper analyzes a two person zero-sum game in which the strategies on the two sides are probability distributions. The solutions always turn out to contain jumps. In most cases the distributions are combinations of delta functions and density functions. The problem is as follows: a submarine chooses a range r, within a declared war zone, at which to fire his missile. If he is detected at a larger range he attempts to fire at that larger range with the effectiveness at that range decreased by defense measures such as attempts to kill the submarine, shoot down the missle, or protect the target. If this defense effectiveness is denoted by omega, with omega = 0 referring to perfect defensive reaction measures, and omega = 1 referring to poor defensive reaction measures, the following is true. If omega = 0, the problem is analogous to a problem ('The Two Machine-gun Duel') solved by L. Gillman and the author in 1949 (Ref. 2) and is not difficult. The defenses in this case are in close to the coast. If omega = 1 the problem is different but not difficult and the defenses are well out towards (and in some cases at) maximum missile range. There are for omega = 1 no defenses near the coast; this is referred to as an 'initial gap.'

Descriptors :   (*GAME THEORY, STATISTICAL DISTRIBUTIONS), (*ANTIMISSILE DEFENSE SYSTEMS, MILITARY STRATEGY), (*MILITARY STRATEGY, GAME THEORY), ANTISUBMARINE DEFENSE SYSTEMS

Distribution Statement : APPROVED FOR PUBLIC RELEASE