# Learning Nash Equilibria in Monotone Games

arXiv: https://arxiv.org/abs/1904.01882 · HTML: https://mlsanity.com/paper/1904.01882/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Apr 2019.

## Built on by (most cited first, 11 of 11)

- [Multiplayer Performative Prediction: Learning in Decision-Dependent Games](https://mlsanity.com/paper/2201.03398/) (2022)
- [A unified stochastic approximation framework for learning in games](https://mlsanity.com/paper/2206.03922/) (2022)
- [Adaptively Perturbed Mirror Descent for Learning in Games](https://mlsanity.com/paper/2305.16610/) (2023)
- [Asymptotic Convergence and Performance of Multi-Agent Q-Learning Dynamics](https://mlsanity.com/paper/2301.09619/) (2023)
- [Learning to Control Unknown Strongly Monotone Games](https://mlsanity.com/paper/2407.00575/) (2024)
- [Efficient Uncoupled Learning Dynamics with tildeO!left(T-1/4right) Last-Iterate Convergence in Bilinear Saddle-Point Problems over Convex Sets under Bandit Feedback](https://mlsanity.com/paper/2602.21436/) (2026)
- [Second-Order Mirror Descent: Convergence in Games Beyond Averaging and Discounting](https://mlsanity.com/paper/2111.09982/) (2021)
- [On the Stability of Learning in Network Games with Many Players](https://mlsanity.com/paper/2403.15848/) (2024)
- [An Imitation Learning Based Algorithm Enabling Priori Knowledge Transfer in Modern Electricity Markets for Bayesian Nash Equilibrium Estimation](https://mlsanity.com/paper/2305.06924/) (2023)
- [Stability of Multi-Agent Learning: Convergence in Network Games with Many Players](https://mlsanity.com/paper/2307.13922/) (2023)
- [Last-Iterate Guarantees for Learning in Co-coercive Games](https://mlsanity.com/paper/2604.19065/) (2026)

## Abstract (arXiv)

We consider multi-agent decision making where each agent's cost function depends on all agents' strategies. We propose a distributed algorithm to learn a Nash equilibrium, whereby each agent uses only obtained values of her cost function at each joint played action, lacking any information of the functional form of her cost or other agents' costs or strategy sets. In contrast to past work where convergent algorithms required strong monotonicity, we prove algorithm convergence under mere monotonicity assumption. This significantly widens algorithm's applicability, such as to games with linear coupling constraints.