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.

我们开始研究经典连续上校布洛托游戏的自然多人泛化。由 Borel (1953) 引入的两人 Blotto 游戏作为跨n 个同时战线的资源竞争模型，已被广泛研究了一个世纪，并在整个社会科学中得到了大量应用。我们的工作定义了多人上校 Blotto 游戏，并针对k（玩家数量）和n 的各种设置推导出纳什均衡. 我们还介绍了 Blotto 的“布尔”版本，它在多人游戏设置中变得有趣。正如在两人理论文献中一样，我们工作的主要技术难点是将各种边际分布耦合成满足严格总和约束的联合分布的挑战。与之前在连续设置中的工作相比，我们以高效采样算法的形式在算法上推导出我们的耦合。