# Oleft(1/Tright) Time-Average Convergence in a Generalization of Multiagent Zero-Sum Games

arXiv: https://arxiv.org/abs/2110.02482 · HTML: https://mlsanity.com/paper/2110.02482/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Oct 2021.

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

- [Asynchronous Gradient Play in Zero-Sum Multi-agent Games](https://mlsanity.com/paper/2211.08980/) (2022)
- [A Survey of Decision Making in Adversarial Games](https://mlsanity.com/paper/2207.07971/) (2022)
- [Characterizing Nash Equilibria in Zero-Sum Games: A Physics-Inspired, Parallelizable Approach with a Linear Number of Gradient Queries](https://mlsanity.com/paper/2507.11366/) (2025)

## Abstract (arXiv)

We introduce a generalization of zero-sum network multiagent matrix games and prove that alternating gradient descent converges to the set of Nash equilibria at rate O(1/T) for this set of games. Alternating gradient descent obtains this convergence guarantee while using fixed learning rates that are four times larger than the optimistic variant of gradient descent. Experimentally, we show with 97.5% confidence that, on average, these larger learning rates result in time-averaged strategies that are 2.585 times closer to the set of Nash equilibria than optimistic gradient descent.