# Distributionally Robust Nash Equilibria via Variational Inequalities

arXiv: https://arxiv.org/abs/2510.17024 · HTML: https://mlsanity.com/paper/2510.17024/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Oct 2025.

## Built on by (most cited first, 2 of 2)

- [Wasserstein Distributionally Robust Nash Equilibrium Seeking with Heterogeneous Data: A Lagrangian Approach](https://mlsanity.com/paper/2511.14048/) (2025)
- [Strategically Robust Multi-Agent Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/2603.09208/) (2026)

## Abstract (arXiv)

Nash Equilibrium and its robust counterpart, Distributionally Robust Nash Equilibrium (DRNE), are fundamental problems in game theory with applications in economics, engineering, and machine learning. This paper addresses the problem of DRNE, where multiple players engage in a noncooperative game under uncertainty. Each player aims to minimize their objective against the worst-case distribution within an ambiguity set, resulting in a minimax structure. We reformulate the DRNE problem as a Variational Inequality (VI) problem, providing a unified framework for analysis and algorithm development. We propose a gradient descent-ascent type algorithm with convergence guarantee that effectively addresses the computational challenges of high-dimensional and nonsmooth objectives.