The multiplayer Colonel Blotto game

• 成果类型: Article
• 署名作者: Boix-Adsera, Enric; Edelman, Benjamin L.; Jayanti, Siddhartha
• 署名单位: Massachusetts Institute of Technology (MIT); Harvard University; Massachusetts Institute of Technology (MIT)
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2021.05.002
• 发表日期: 2021
• 页码: 15-31
• 关键词: Multiplayer equilibria; blotto game; Equilibrium computation; Multiparty elections

摘要

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. (C) 2021 Elsevier Inc. All rights reserved.