Distributionally Robust Nash Equilibrium Seeking with Partial Observations and Distributed Communication

2026-05-15

AI Summary

This work addresses the problem of computing distributionally robust Nash equilibria (DRoNE) in multi-agent systems under partial observability and directed communication networks, where only a finite set of independent and identically distributed samples from an unknown true distribution is available. The authors propose a modeling framework that maximizes worst-case expected utility over a Wasserstein ambiguity set and develop the Inertial Support Best Response Algorithm (ISBRAG) along with its distributed variant, d-ISBRAG. This study establishes, for the first time, a distributed solution method for DRoNE under partial observability and directed communication, provides theoretical guarantees on the existence of DRoNE and its convergence to the Nash equilibrium of the underlying stochastic game as the sample size grows, and validates the efficacy of the proposed algorithms through simulations in both individual and shared sampling scenarios.

Abstract

In this work, we study stochastic one-shot games where agents'utilities depend on the collective strategy profiles of other agents as well as on some well-behaved randomness. While each decision-maker is agnostic to the random variable's underlying distribution, they have access to finitely many i.i.d. samples generated from it. We consider two cases: one where samples are shared; and another, more special one, where samples are individually accessible. To hedge against the unknown uncertainty, each agent plays a distributionally robust game and aims to maximize the worst-case expected utility over a Wasserstein ball around the sample average distribution. In this setting, we provide conditions under which the game has a non-empty set of distributionally robust Nash equilibria (DRoNE) and then characterize the closeness of the DRoNE set to the Nash equilibria (NE) of the associated stochastic game. We then propose an inertial, supported, better response, ascending supergradient dynamics ISBRAG that seeks the DRoNE's when the distributionally robust game possesses what we term as amicable supergradients. This forms the basis of a distributed version (d-ISBRAG) where agents estimate others'strategies by means of a dynamic consensus subroutine over a directed communication network. While initially the distributed algorithm works in the case where agents have individual samples, we later extend this to the case of shared observations under certain simplifying assumptions. This involves analyzing a tractable reformulation of the distributionally robust optimization problem and solving it in a distributed manner to compute the required supergradients. Simulations illustrate our results.

Problem

• Distributionally Robust Optimization
• Nash Equilibrium
• Partial Observations
• Stochastic Games
• Wasserstein Ambiguity

Innovation

• Distributionally Robust Optimization
• Nash Equilibrium Seeking
• Wasserstein Ambiguity Set
• Distributed Consensus
• Supergradient Dynamics