An Algorithmic Solution to the Blotto Game Using Multimarginal Couplings

Abstract

Computing the solution of Blotto games, a century-year-old open problem The Blotto game has been introduced by Borel more than a century ago in a seminal game theory paper. Surprisingly, characterizing and computing the optimal solutions (or the Nash equilibria) of this game in general was still open! This paper combines theoretical tools from statistics and auction theory to provide an almost explicit characterization of the strategies that are then computed using techniques from optimal transport (and other algorithmic ideas). The complexity of the final algorithm is even polynomial in the number of battlefields (a key parameter of a Blotto game) and the approximation level.