  This paper explores the Nash equilibria of a variant of the Colonel Blotto
game, which we call the Asymmetric Colonel Blotto game. In the Colonel Blotto
game, two players simultaneously distribute forces across $n$ battlefields.
Within each battlefield, the player that allocates the higher level of force
wins. The payoff of the game is the proportion of wins on the individual
battlefields. In the asymmetric version, the levels of force distributed to the
battlefields must be nondecreasing. In this paper, we find a family of Nash
equilibria for the case with three battlefields and equal levels of force and
prove the uniqueness of the marginal distributions. We also find the unique
equilibrium payoff for all possible levels of force in the case with two
battlefields, and obtain partial results for the unique equilibrium payoff for
asymmetric levels of force in the case with three battlefields.
