On Suboptimal Solution of Antagonistic Matrix Games

The paper examines resource allocation games such as Colonel Blotto and Colonel Lotto games with the goal to develop tractable method for building suboptimal solution in mixed strategies of these games without solving the relevant optimization problem. The foundation of proposed method lies in the specific combinatorial properties of the partition games. It turned out that as far as distribution of resource along battlefield is concerned that pure strategies participating in ε-optimal solution possessed specific structure. Numerical experiments showed that these specific structural peculiarities can be easily reproduced utilizing previously found combinatorial properties of partition. As a result, we get ε-optimal solution of partition games and support set mixed strategies can be computed in polynomial time