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arXiv · 2002.05240

The Multiplayer Colonel Blotto Game

Enric Boix-Adserà·Benjamin L. Edelman·Siddhartha Jayanti
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Abstract

We initiate the study of the natural multiplayer generalization of the classic continuous Colonel Blotto game. The two-player Blotto game, introduced by Borel as a model of resource competition across $n$ simultaneous fronts, has been studied extensively for a century and seen numerous applications throughout the social sciences. Our work defines the multiplayer Colonel Blotto game and derives Nash equilibria for various settings of $k$ (number of players) and $n$. We also introduce a "Boolean" version of Blotto that becomes interesting in the multiplayer setting. The main technical difficulty of our work, as in the two-player theoretical literature, is the challenge of coupling various marginal distributions into a joint distribution satisfying a strict sum constraint. In contrast to previous works in the continuous setting, we derive our couplings algorithmically in the form of efficient sampling algorithms.

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Enric Boix-Adserà, Benjamin L. Edelman, Siddhartha Jayanti. 2020-02-12. The Multiplayer Colonel Blotto Game. https://arxiv.org/abs/2002.05240

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