# Exponential Convergence of Gradient Methods in Concave Network Zero-sum Games

arXiv: https://arxiv.org/abs/2007.05477 · HTML: https://mlsanity.com/paper/2007.05477/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jul 2020.

## Built on by (most cited first, 4 of 4)

- [Asymptotic Convergence and Performance of Multi-Agent Q-Learning Dynamics](https://mlsanity.com/paper/2301.09619/) (2023)
- [On the Stability of Learning in Network Games with Many Players](https://mlsanity.com/paper/2403.15848/) (2024)
- [Stability of Multi-Agent Learning: Convergence in Network Games with Many Players](https://mlsanity.com/paper/2307.13922/) (2023)
- [Stability of Multi-Agent Learning in Competitive Networks: Delaying the Onset of Chaos](https://mlsanity.com/paper/2312.11943/) (2023)

## Abstract (arXiv)

Motivated by Generative Adversarial Networks, we study the computation of Nash equilibrium in concave network zero-sum games (NZSGs), a multiplayer generalization of two-player zero-sum games first proposed with linear payoffs. Extending previous results, we show that various game theoretic properties of convex-concave two-player zero-sum games are preserved in this generalization. We then generalize last iterate convergence results obtained previously in two-player zero-sum games. We analyze convergence rates when players update their strategies using Gradient Ascent, and its variant, Optimistic Gradient Ascent, showing last iterate convergence in three settings -- when the payoffs of players are linear, strongly concave and Lipschitz, and strongly concave and smooth. We provide experimental results that support these theoretical findings.