Non-symmetric discrete Colonel Blotto game

We study equilibrium strategies and the value of the asymmetric variant of the discrete Colonel Blotto game with $K\ge 2$ battlefields, $B\ge 1$ resources of the weaker player and $A>B$ resources of the stronger player. We derive equilibrium strategies and the formulas for the value of the game for the cases where the number of resources of the weaker player, $B$, is at least $2(\lceil A\mathrm{/}K\rceil -1)$ as well as for the cases where this number is at most $\lfloor A\mathrm{/}K\rfloor$. In particular, we solve all the cases of the game which can be solved using the discrete General Lotto game of~\cite{Hart08}. We propose a constrained variant of the discrete General Lotto game and use it to derive equilibrium strategies in the discrete Colonel Blotto game, that go beyond the General Lotto solvable cases game.