# Learning Generalized Nash Equilibria in a Class of Convex Games

arXiv: https://arxiv.org/abs/1703.04113 · HTML: https://mlsanity.com/paper/1703.04113/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Mar 2017.

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

- [A unified stochastic approximation framework for learning in games](https://mlsanity.com/paper/2206.03922/) (2022)
- [Risk-Averse No-Regret Learning in Online Convex Games](https://mlsanity.com/paper/2203.08957/) (2022)
- [Expected Variational Inequalities](https://mlsanity.com/paper/2502.18605/) (2025)
- [Decentralized Bandit Learning of Markov Perfect Equilibria](https://mlsanity.com/paper/2610.14333/) (2026)

## Abstract (arXiv)

We consider multi-agent decision making where each agent optimizes its convex cost function subject to individual and coupling constraints. The constraint sets are compact convex subsets of a Euclidean space. To learn Nash equilibria, we propose a novel distributed payoff-based algorithm, such that each agent uses information only about its cost function values and the constraint function values with their associated dual multiplier. We prove convergence of this algorithm to a Nash equilibrium, under the assumption that the game admits a strictly convex potential function. In the absence of coupling constraints, we prove convergence to Nash equilibria under significantly weaker assumptions, not requiring a potential function. Namely, strict monotonicity of the game mapping is sufficient for convergence. We also derive the convergence rate of the algorithm for strongly monotone game maps.