On the theory of stochastic duels

Abstract

This thesis is concerned with the theory of stochastic duels that include various limiting factors of real combat situations. In one versus one duel, the "fundamental duel" studied by Williams and Ancker is extended to include various limiting factors of weapon, combat and combat-support capabilities. These factors are rate of fire, single shot hit (kill) probability, single pattern or salvo kill probability, a sure kill by multiple hits, conditional kill probability on hit, volume of a pattern, a salvo or a dispenser, random surprise, random detection, the limitation of duel time, the limitation of ammunition supply and so forth. A particular emphasis is placed on multiple hits and detection capability. In duels with more than two combatants, the probabilistic linear, square and mixed laws studied by Brown and others are extended to include the limitation of battle time under the assumption that interfiring times are continuous random variables. In addition, several multiple duel models with continuous interfiring times are constructed and relative efficiencies of strategies such as standby, concentrated, individually separated and random firings are investigated. The results obtained in this thesis may be utilized in evaluating weapon, combat and combat-support capabilities, in designing a set of optimal levels of weapon effectiveness parameters, and in comparing tactics and strategies related to weapon characteristics.