# A survey on algorithms for Nash equilibria in finite normal-form games

arXiv: https://arxiv.org/abs/2312.11063 · HTML: https://mlsanity.com/paper/2312.11063/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 109 references that are in the map.
- First posted on arXiv 18 Dec 2023.

## Builds on (most cited first, 3 of 3)

- [Dota 2 with Large Scale Deep Reinforcement Learning](https://mlsanity.com/paper/1912.06680/) (2019)
- [Suphx: Mastering Mahjong with Deep Reinforcement Learning](https://mlsanity.com/paper/2003.13590/) (2020)
- [On Convergence Lemma and Convergence Stability for Piecewise Analytic Functions](https://mlsanity.com/paper/2204.01643/) (2022)

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

- [A Survey on Self-play Methods in Reinforcement Learning](https://mlsanity.com/paper/2408.01072/) (2024)
- [Discovering Expert-Level Nash Equilibrium Algorithms with Large Language Models](https://mlsanity.com/paper/2508.11874/) (2025)
- [On the Geometry of Games and their Solvers](https://mlsanity.com/paper/2605.29919/) (2026)

## Abstract (arXiv)

Nash equilibrium is one of the most influential solution concepts in game theory. With the development of computer science and artificial intelligence, there is an increasing demand on Nash equilibrium computation, especially for Internet economics and multi-agent learning. This paper reviews various algorithms computing the Nash equilibrium and its approximation solutions in finite normal-form games from both theoretical and empirical perspectives. For the theoretical part, we classify algorithms in the literature and present basic ideas on algorithm design and analysis. For the empirical part, we present a comprehensive comparison on the algorithms in the literature over different kinds of games. Based on these results, we provide practical suggestions on implementations and uses of these algorithms. Finally, we present a series of open problems from both theoretical and practical considerations.