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K-Round Duel with Uneven Resource Distribution

Volume 8, Number 1, January 2012 - Paper 2 - pp. 19-34


1 The Israel Electric Corporation Ltd, Israel
2 Faculty of Social Sciences, University of Stavanger, Norway

(Received on August 14, 2009, and revised May 27, 2010)


The paper considers optimal resource distribution between offense and defense and among different rounds in a K-round duel. In each round of the duel, two actors exchange attacks. Each actor allocates resources into attacking the counterpart and into defending itself against the counterpart's attack. The offense resources are expendable (e.g., missiles), whereas the defense resources are not expendable (e.g., bunkers). Offense distribution across rounds can increase or decrease as determined by a geometric series. The outcomes of each round are determined by a contest success functions which depend on the offensive vs. defensive resources ratio. The game ends when at least one target is destroyed or after K rounds. It is shown 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. When both actors can choose their offense resource distribution freely, they distribute all offense to the first round. When one actor is constrained to distribute offense resources across multiple rounds, it is not necessarily optimal for the other actor to allocate all offense to the first round. We illustrate how the resources, contest intensities and number of rounds in the duels impact the survivabilities and resource distributions.


References: 19

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