On computing nash equilibria of Borel's Colonel Blotto Game for multiple players including in arbitrary measure spaces

Abstract

The Colonel Blotto Problem proposed by Borel in 1921 has served as a widely applicable model of budget-constrained simultaneous winner-take-all competitions in the social sciences. Applications include elections, advertising, research and development, ecology and more. However, the classic Blotto problem and variants that have been studied hereto are only about two-player games on a finite set of discrete battlefields. This thesis extends the classic theory to multiplayer games over arbitrary measureable battlegrounds. Furthermore, it characterizes the symmetric mixed Nash equilibria of a wide array of these generalized Blotto games and provides efficient algorithms to sample from these equilibria; thereby unleashing the potential for quantitative analyses of a multitude of new and significant applications, such as multiparty elections and ideological battles across the surface of the earth.