  This paper analyzes the structure of mixed-strategy equilibria for Colonel
Blotto games, where the outcome on each battlefield is a polynomial function of
the difference between the two players' allocations. This paper severely
reduces the set of strategies that needs to be searched to find a Nash
equilibrium. It finds that there exists a Nash equilibrium where both players'
mixed strategies are discrete distributions, and it places an upper bound on
the number of points in the supports of these discrete distributions.
