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

TL;DR

This paper develops a scalable method to find Nash equilibria in Wasserstein distributionally robust games with heterogeneous data, using finite-dimensional reformulations and efficient algorithms, demonstrated through simulations.

Contribution

It introduces a finite-dimensional reformulation of Wasserstein distributionally robust Nash games, enabling scalable computation of equilibria with fixed constraints regardless of sample size.

Findings

Finite-dimensional reformulation of the game problem.

Algorithms based on the golden ratio for equilibrium computation.

Validated scalability and efficiency through simulations.

Abstract

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.