# The Multiplayer Colonel Blotto Game

arXiv: https://arxiv.org/abs/2002.05240 · HTML: https://mlsanity.com/paper/2002.05240/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2020.

## Built on by (most cited first, 2 of 2)

- [A Survey of Decision Making in Adversarial Games](https://mlsanity.com/paper/2207.07971/) (2022)
- [Finding mixed-strategy equilibria of continuous-action games without gradients using randomized policy networks](https://mlsanity.com/paper/2211.15936/) (2022)

## Abstract (arXiv)

We initiate the study of the natural multiplayer generalization of the classic continuous Colonel Blotto game. The two-player Blotto game, introduced by Borel as a model of resource competition across n simultaneous fronts, has been studied extensively for a century and seen numerous applications throughout the social sciences. Our work defines the multiplayer Colonel Blotto game and derives Nash equilibria for various settings of k (number of players) and n. We also introduce a "Boolean" version of Blotto that becomes interesting in the multiplayer setting. The main technical difficulty of our work, as in the two-player theoretical literature, is the challenge of coupling various marginal distributions into a joint distribution satisfying a strict sum constraint. In contrast to previous works in the continuous setting, we derive our couplings algorithmically in the form of efficient sampling algorithms.