Pure Strategy Nash Equilibrium in 2-Contestant Generalized Lottery Colonel Blotto Games

We consider a large class of 2-contestant Colonel Blotto games, for which the budget and valuation are both asymmetric between players and the contest success functions are in Tullock form with battle-specific discriminatory power in (0, 1] and battle-and-contestant-specific lobbying effectiveness. We prove the existence of pure strategy Nash Equilibrium of the game through a direct equilibrium characterization approach. We examine some important equilibrium properties. Among them, the rate of equilibrium rent dissipation ratio between the two contestants is constant across all the battles, and the payoff dominance relationship is impossible between any two distinct equilibria. Furthermore, we provide two sets of sufficient conditions, under each of which the equilibrium of the game is unique. Our study contributes to a better understanding regarding both the existence and the uniqueness, as well as characterization and properties, of equilibria in Blotto games