Shield versus sword resource distribution in K-round duels

Collaborative Autonomic Computing Laboratory, School of Computer Science, University of Electronic Science and Technology of China, Chengdu, People’s Republic of China
Central European Journal of Operations Research (Impact Factor: 0.83). 12/2011; 19(4):589-603. DOI: 10.1007/s10100-010-0148-5


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.

KeywordsSurvivability–Duel–Defense–Attack–Protection–Contest intensity–Game theory

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    ABSTRACT: Hausken (2008a) formulates a contest-theoretic model of the attack and defense of a network of targets. This note identi es a technical error that invalidates Hausken's characterization of Nash equilibrium for a substantial portion of the parameter space that he examines and provides necessary conditions for his solution to form a pure- strategy Nash equilibrium. Many of the existing results in the contest-theoretic liter- ature on the attack and defense of networks of targets rely upon Hausken's (2008a) characterization and require corresponding parameter restrictions. When these restric- tions are not met, the analysis of Clark and Konrad (2007) and Kovenock and Roberson (2010a) provides a foundation for constructing mixed-strategy Nash equilibria.
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