The Multiplayer Colonel Blotto Game

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 nsimultaneous fronts, has been studied extensively for a century and seen numerous applications throughout the social sciences. Our work defines the multiplayer Colonel Blotto gameand derives Nash equilibria for various settings of k(number of players) and n(number of battlefields)---in particular, we mostly solve the symmetric three-player case. We also introduce a Boolean version of multiplayer Blotto. 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. The full paper can be found at https://arxiv.org/abs/2002.05240.