Abstract
In this paper, we consider a 4-player, two stage Colonel Blotto game in which one player, the attacker, simultaneously participates in three disjoint Colonel Blotto games against three defenders. During the first stage of the game, the defenders can choose to form independent coalitions by transferring resources (troops, funds, computing resources, etc.) among each other if the transfer benefits the defenders involved. In the second stage, the attacker observes these transfers among defenders and then allocates a portion of his overall resources to fight against each defender. We find that the formation of coalitions depends on both the ratios of resources between the attacker and the defenders and on each defender’s total battlefield value to resource ratio. For one parameter region, we completely characterize the subgame-perfect Nash equilibrium. For another parameter region, we show that there are parameters of the game for which transfers occur and provide a computational method to calculate those transfers.
The first author was fully supported by the United States Military Academy and the Army Advanced Civil Schooling (ACS) program.
The second author gratefully acknowledges support from NSF Grant 1565487.
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Heyman, J.L., Gupta, A. (2018). Colonel Blotto Game with Coalition Formation for Sharing Resources. In: Bushnell, L., Poovendran, R., Başar, T. (eds) Decision and Game Theory for Security. GameSec 2018. Lecture Notes in Computer Science(), vol 11199. Springer, Cham. https://doi.org/10.1007/978-3-030-01554-1_10
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