Non-symmetric discrete Colonel Blotto game

TL;DR

This paper analyzes equilibrium strategies and game value for an asymmetric discrete Colonel Blotto game with multiple battlefields and resource asymmetry, extending solutions beyond previously solvable cases using a novel constrained General Lotto approach.

Contribution

It derives equilibrium strategies and formulas for the asymmetric discrete Colonel Blotto game in new parameter regimes, expanding beyond known solvable cases with a novel constrained General Lotto method.

Findings

Derived equilibrium strategies for specific resource configurations.

Provided formulas for the game value in new parameter regimes.

Extended the solvable cases of the discrete Colonel Blotto game.

Abstract

We study equilibrium strategies and the value of the asymmetric variant of the discrete Colonel Blotto game with $K \geq 2$ battlefields, $B \geq 1$ 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 $2(\lceil A/K \rceil - 1)$ as well as for the cases where this number is at most $\lfloor A/K \rfloor$. 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.