Fast and Simple Solutions of Blotto Games

Abstract

The Colonel Blotto game (initially introduced by Borel in 1921) is commonly used for analyzing a wide range of applications from the U.S.Ppresidential election to innovative technology competitions to advertising, sports, and politics. After around a century Ahmadinejad et al. provided the first polynomial-time algorithm for computing the Nash equilibria in Colonel Blotto games. However, their algorithm consists of an exponential-size LP solved by the ellipsoid method, which is highly impractical. In “Fast and Simple Solutions of Blotto Games,” Behnezhad, Dehghani, Derakhshan, Hajighayi, and Seddighin provide the first polynomial-size LP formulation of the optimal strategies for the Colonel Blotto game using linear extension techniques. They use this polynomial-size LP to provide a simpler and significantly faster algorithm for finding optimal strategies of the Colonel Blotto game. They further show this representation is asymptotically tight, which means there exists no other linear representation of the strategy space with fewer constraints.