# A Partial Solution to Continuous Blotto

## TL;DR

This paper investigates mixed-strategy equilibria in Colonel Blotto games with polynomial outcome functions, showing that equilibrium strategies can be discrete and providing bounds on their support sizes.

## Contribution

It introduces a significant reduction in the strategy search space and proves the existence of discrete equilibrium strategies with bounded support.

## Key findings

- Existence of Nash equilibrium with discrete strategies
- Upper bounds on the number of support points in equilibrium
- Reduction of strategy search space in Blotto games

## Abstract

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.