A Partial Solution to Continuous Blotto
Provides theoretical advances for game theorists studying Colonel Blotto games, though incremental as it extends known results to polynomial payoffs.
The paper reduces the search space for Nash equilibria in Colonel Blotto games with polynomial payoff functions, proving existence of equilibria with discrete mixed strategies and bounding the support size.
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.