Lanchester Model for Three-Way Combat

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Authors
Grass, Dieter
Kress, Moshe
Caulkins, Jonathan P.
Feichtinger, Gustav
Seidl, Andrea
Subjects
Advisors
Date of Issue
2017-01
Date
Research Report 2017-02
Publisher
Monterey, California. Naval Postgraduate School
Language
Abstract
Lanchester (1916) modeled combat situations between two opponents, where mutual attrition occurs continuously in time, by a pair of simple ordinary (linear) differential equations. The aim of the present paper is to extend the model to a conflict consisting of three parties. In particular, Lanchester's main result, i.e. his square law, is adapted to a triple fight. However, here a central factor besides the initial strengths of the forces determining the long run outcome is the allocation of each opponent's efforts between the other two parties. De- pending on initial strengths, (the) solution paths are calculated and visualized in appropriate phase portraits. We are able identify regions in the state space where, independent of the force allocation of the opponents, always the same combatant wins, regions, where a combatant can win if its force allocation is wisely chosen, and regions where a combatant cannot win itself but determine the winner by its forces allocation. As such, the present model can be seen as a forerunner of a dynamic game between three opponents.
Type
Report
Description
Department
Operations Research (OR)
Organization
Naval Postgraduate School (U.S.)
Carnegie Mellon University
Vienna University of Technology
University of Vienna
Identifiers
NPS Report Number
Sponsors
Naval Research Program
This research was supported by the Austrian Science Fund (FWF)
Funder
P25979-N25
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Citation
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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