An essay on Multiplayer Colonel Blotto Game

Abstract

We consider a Colonel Blotto game with complete information and analyze it over multiple battlefields. Resources among players are symmetric and there exists full information on the budget constraints of the players. Given a general ratio contest success function we derive the pure strategy symmetric Nash equilibrium. The valuations of battlefields are ordered in a way that, at equilibrium the marginal utility of additional resources to players remains the same across all battlefields that have positive allocations.