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

2025-11-17

AI Summary

This paper studies heterogeneous distributionally robust games, where agents operate under non-shared uncertainty assumptions and independently select distinct Wasserstein ball radii to express individualized distributional robustness preferences. We propose a unified modeling framework based on Lagrangian duality, equivalently reformulating the original problem as a strongly monotone variational inequality. A distributed iterative algorithm is designed, with theoretical guarantees that the average regret converges to zero as the number of iterations increases, and that a robust Nash equilibrium within a prescribed accuracy is attained in finite steps. To the best of our knowledge, this is the first work to achieve equilibrium computation under heterogeneous risk aversion and non-shared distributional shifts, thereby overcoming the restrictive homogeneity assumption prevalent in conventional distributionally robust game theory. Numerical experiments validate the method’s convergence properties and robust performance.

Technology Category

• Game Theory and Economic Paradigms: Adversarial Learning
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

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.

Problem

• Studying distributionally robust games with heterogeneous agent risk aversion
• Formulating Nash equilibrium via variational inequality with monotone mapping
• Designing algorithm to learn approximate equilibrium with diminishing regret

Innovation

• Lagrangian formulation for Wasserstein constraints
• Variational inequality with strong monotonicity
• Approximate Nash equilibrium with diminishing regret