# Stochastic generalized Nash equilibrium seeking in merely monotone games

arXiv: https://arxiv.org/abs/2002.08318 · HTML: https://mlsanity.com/paper/2002.08318/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Feb 2020.

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

- [Finite-sample guarantees for data-driven forward-backward operator methods](https://mlsanity.com/paper/2512.19172/) (2025)
- [No-regret learning for repeated non-cooperative games with lossy bandits](https://mlsanity.com/paper/2205.06968/) (2022)
- [Wasserstein Distributionally Robust Nash Equilibrium Seeking with Heterogeneous Data: A Lagrangian Approach](https://mlsanity.com/paper/2511.14048/) (2025)

## Abstract (arXiv)

We solve the stochastic generalized Nash equilibrium (SGNE) problem in merely monotone games with expected value cost functions. Specifically, we present the first distributed SGNE seeking algorithm for monotone games that requires one proximal computation (e.g., one projection step) and one pseudogradient evaluation per iteration. Our main contribution is to extend the relaxed forward-backward operator splitting by Malitsky (Mathematical Programming, 2019) to the stochastic case and in turn to show almost sure convergence to a SGNE when the expected value of the pseudogradient is approximated by the average over a number of random samples.