# Nash equilibrium seeking for a class of quadratic-bilinear Wasserstein distributionally robust games

arXiv: https://arxiv.org/abs/2411.09636 · HTML: https://mlsanity.com/paper/2411.09636/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Nov 2024.

## Built on by (most cited first, 1 of 1)

- [Wasserstein Distributionally Robust Nash Equilibrium Seeking with Heterogeneous Data: A Lagrangian Approach](https://mlsanity.com/paper/2511.14048/) (2025)

## Abstract (arXiv)

We consider a class of Wasserstein distributionally robust Nash equilibrium problems, where agents construct heterogeneous data-driven Wasserstein ambiguity sets using private samples and radii, in line with their individual risk-averse behaviour. By leveraging relevant properties of this class of games, we show that equilibria of the original seemingly infinite-dimensional problem can be obtained as a solution to a finite-dimensional Nash equilibrium problem. We then reformulate the problem as a finite-dimensional variational inequality and establish the connection between the corresponding solution sets. Our reformulation has scalable behaviour with respect to the data size and maintains a fixed number of constraints, independently of the number of samples. To compute a solution, we leverage two algorithms, based on the golden ratio algorithm. The efficiency of both algorithmic schemes is corroborated through extensive simulation studies on an illustrative example and a stochastic portfolio allocation game, where behavioural coupling among investors is modeled.