From Duels to Battlefields: Computing Equilibria of Blotto and Other Games

In the well-studied Colonel Blotto game, players must divide a pool of troops among a set of battlefields with the goal of winning a majority. Despite the importance of this game, only a few solutions for special variants of the problem are known. We provide a general technique for computing equilibria of the Colonel Blotto game. Our approach applies to variations of the Colonel Blotto game as well, including an infinite-strategy variant called the General Lotto game. We also apply our technique beyond Colonel Blotto games to create the first polynomial-time algorithms for computing equilibria for a variety of other zero-sum games. Our approach is to reformulate each zero-sum game into a bilinear form, then reduce equilibrium computation to linear optimization over a game-specific polytope.