# Algorithm for Computing Approximate Nash Equilibrium in Continuous Games with Application to Continuous Blotto

arXiv: https://arxiv.org/abs/2006.07443 · HTML: https://mlsanity.com/paper/2006.07443/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2020.

## Built on by (most cited first, 3 of 3)

- [Finding mixed-strategy equilibria of continuous-action games without gradients using randomized policy networks](https://mlsanity.com/paper/2211.15936/) (2022)
- [ApproxED: Approximate exploitability descent via learned best responses](https://mlsanity.com/paper/2301.08830/) (2023)
- [DiffNash: Finding Nash Equilibrium in High-Dimensional Continuous Action Spaces with Diffusion Policies](https://mlsanity.com/paper/2610.15932/) (2026)

## Abstract (arXiv)

Successful algorithms have been developed for computing Nash equilibrium in a variety of finite game classes. However, solving continuous games -- in which the pure strategy space is (potentially uncountably) infinite -- is far more challenging. Nonetheless, many real-world domains have continuous action spaces, e.g., where actions refer to an amount of time, money, or other resource that is naturally modeled as being real-valued as opposed to integral. We present a new algorithm for {approximating} Nash equilibrium strategies in continuous games. In addition to two-player zero-sum games, our algorithm also applies to multiplayer games and games with imperfect information. We experiment with our algorithm on a continuous imperfect-information Blotto game, in which two players distribute resources over multiple battlefields. Blotto games have frequently been used to model national security scenarios and have also been applied to electoral competition and auction theory. Experiments show that our algorithm is able to quickly compute close approximations of Nash equilibrium strategies for this game.