Existence of a unique Nash equilibrium for an asymmetric lottery Blotto game with weighted majority

We consider an asymmetric lottery Blotto game with two agents and n items, where both agents wish to maximize their probability of winning a majority value of all n items. Duffy and Matros [2] showed that if there exists a Nash equilibrium, then the equilibrium is unique, and it is found in an explicit expression. They also provided sufficient conditions for the existence of a Nash equilibrium in the cases of n = 3 and n = 4 . In this paper, we prove that the lottery Blotto game always has a unique Nash equilibrium for any value of n.