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The multiplayer Colonel Blotto game

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  • Boix-Adserà, Enric
  • Edelman, Benjamin L.
  • Jayanti, Siddhartha

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 (1953) as a model of resource competition across n simultaneous fronts, has been studied extensively for a century and has 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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  • Boix-Adserà, Enric & Edelman, Benjamin L. & Jayanti, Siddhartha, 2021. "The multiplayer Colonel Blotto game," Games and Economic Behavior, Elsevier, vol. 129(C), pages 15-31.
    • Handle: RePEc:eee:gamebe:v:129:y:2021:i:c:p:15-31
    DOI: 10.1016/j.geb.2021.05.002
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    1. Li, Xinmi & Zheng, Jie, 2022. "Pure strategy Nash Equilibrium in 2-contestant generalized lottery Colonel Blotto games," Journal of Mathematical Economics, Elsevier, vol. 103(C).

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