Distributionally Robust Equilibria over the Wasserstein Distance for Generalized Nash Game

Abstract

Generalized Nash equilibrium problem (GNEP) is fundamental for practical applications where multiple self-interested agents work together to make optimal decisions. In this work, we study GNEP with shared distributionally robust chance constraints (DRCCs) for incorporating inevitable uncertainties. The DRCCs are defined over the Wasserstein ball, which can be explicitly characterized even with limited sample data. To determine the equilibrium of the GNEP, we propose an exact approach to transform the original computationally intractable problem into a deterministic formulation using the Nikaido-Isoda function. Specifically, we show that when all agents' objectives are quadratic in their respective variables, the equilibrium can be obtained by solving a typical mixed-integer nonlinear programming (MINLP) problem, where the integer and continuous variables are decoupled in both the objective function and the constraints. This structure significantly improves computational tractability, as demonstrated through a case study on the charging station pricing problem.