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Shield versus sword resource distribution in K-round duels

Hausken, Kjell; Levitin, Gregory
Journal article, Peer reviewed
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URI
http://hdl.handle.net/11250/184361
Date
2010-06
Metadata
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  • Vitenskapelige publikasjoner (SV-IMKS) [85]
Original version
Hausken, K. & Levitin, G. (2010) Shield versus sword resource distribution in Kround duels. Central European Journal of Operations Research, 19(4), 589-603   10.1007/s10100-010-0148-5
Abstract
The paper considers optimal resource distribution between offense and

defense in a duel. In each round of the duel two actors exchange attacks distributing

the offense resources equally across K rounds. The offense resources are expendable

(e.g. missiles), whereas the defense resources are not expendable (e.g. bunkers). The

outcomes of each round are determined by a contest success functions which depend

on the offensive and defensive resources. The game ends when at least one target is

destroyed or after K rounds. We show that when each actor maximizes its own survivability,

then both actors allocate all their resources defensively. Conversely, when

each actor minimizes the survivability of the other actor, then both actors allocate all

their resources offensively. We then consider two cases of battle for a single target

in which one of the actors minimizes the survivability of its counterpart whereas the

counterpart maximizes its own survivability. It is shown that in these two cases the

minmax survivabilities of the two actors are the same, and the sum of their resource

fractions allocated to offense is equal to 1. However, their resource distributions are

different. In the symmetric situation when the actors are equally resourceful and the

two contest intensities are equal, then the actor that fights for the destruction of its

counterpart allocates more resources to offense. We demonstrate a methodology of

game analysis by illustrating how the resources, contest intensities and number of

rounds in the duels impact the survivabilities and resource distributions.
Description
The final publication is available at link.springer.com.
Publisher
Springer
Journal
Central European Journal of Operations Research

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