# Wasserstein Distributionally Robust Nash Equilibrium Seeking with Heterogeneous Data: A Lagrangian Approach

arXiv: https://arxiv.org/abs/2511.14048 · HTML: https://mlsanity.com/paper/2511.14048/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 25 references that are in the map.
- First posted on arXiv 18 Nov 2025.

## Builds on (most cited first, 16 of 16)

- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [Golden Ratio Algorithms for Variational Inequalities](https://mlsanity.com/paper/1803.08832/) (2018)
- [Stochastic generalized Nash equilibrium seeking under partial-decision information](https://mlsanity.com/paper/2011.05357/) (2020)
- [Risk-Averse No-Regret Learning in Online Convex Games](https://mlsanity.com/paper/2203.08957/) (2022)
- [Probably Approximately Correct Nash Equilibrium Learning](https://mlsanity.com/paper/1903.10387/) (2019)
- [Learning of Nash Equilibria in Risk-Averse Games](https://mlsanity.com/paper/2403.10399/) (2024)
- [Strategically Robust Game Theory via Optimal Transport](https://mlsanity.com/paper/2507.15325/) (2025)
- [Stochastic generalized Nash equilibrium seeking in merely monotone games](https://mlsanity.com/paper/2002.08318/) (2020)
- [A priori data-driven robustness guarantees on strategic deviations from generalised Nash equilibria](https://mlsanity.com/paper/2304.05308/) (2023)
- [The scenario approach meets uncertain variational inequalities and game theory](https://mlsanity.com/paper/1903.06762/) (2019)
- [Distributed Forward-Backward algorithms for stochastic generalized Nash equilibrium seeking](https://mlsanity.com/paper/1912.04165/) (2019)
- [Probabilistic feasibility guarantees for solution sets to uncertain variational inequalities](https://mlsanity.com/paper/2005.09420/) (2020)
- [Distributionally Robust Nash Equilibria via Variational Inequalities](https://mlsanity.com/paper/2510.17024/) (2025)
- [Asymmetric Feedback Learning in Online Convex Games](https://mlsanity.com/paper/2307.08812/) (2023)
- [On data-driven Wasserstein distributionally robust Nash equilibrium problems with heterogeneous uncertainty](https://mlsanity.com/paper/2312.03573/) (2023)
- [Nash equilibrium seeking for a class of quadratic-bilinear Wasserstein distributionally robust games](https://mlsanity.com/paper/2411.09636/) (2024)

## Abstract (arXiv)

We study a class of distributionally robust games where agents are allowed to heterogeneously choose their risk aversion with respect to distributional shifts of the uncertainty. In our formulation, heterogeneous Wasserstein ball constraints on each distribution are enforced through a penalty function leveraging a Lagrangian formulation. We then formulate the distributionally robust Nash equilibrium problem and show that under certain assumptions it is equivalent to a finite-dimensional variational inequality problem with a strongly monotone mapping. We then design an approximate Nash equilibrium seeking algorithm and prove convergence of the average regret to a quantity that diminishes with the number of iterations, thus learning the desired equilibrium up to an a priori specified accuracy. Numerical simulations corroborate our theoretical findings.