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 payo↵ 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 payo↵ for all possible levels of
force in the case with two battlefields, and obtain partial results for the unique equilibrium
payo↵ for asymmetric levels of force in the case with three battlefields.