On the robustness of equilibria in generalized aggregative games

TL;DR

This paper investigates the robustness of equilibria in uncertain aggregative games, proposing a data-driven scenario approach to certify equilibrium feasibility and develop a semi-decentralized algorithm for assessing violation probabilities.

Contribution

It introduces a novel scenario-based method for evaluating equilibrium robustness in uncertain aggregative games with linear coupling constraints.

Findings

Provides a feasibility certification method for equilibria under uncertainty.

Develops a semi-decentralized algorithm for assessing violation probabilities.

Demonstrates the approach with an academic example.

Abstract

We address the problem of assessing the robustness of the equilibria in uncertain, multi-agent games. Specifically, we focus on generalized Nash equilibrium problems in aggregative form subject to linear coupling constraints affected by uncertainty with a possibly unknown probability distribution. Within a data-driven context, we apply the scenario approach paradigm to provide a-posteriori feasibility certificates for the entire set of generalized Nash equilibria of the game. Then, we show that assessing the violation probability of such set merely requires to enumerate the constraints that ``shape'' it. For the class of aggregative games, this results in solving a feasibility problem on each active facet of the feasibility region, for which we propose a semi-decentralized algorithm. We demonstrate our theoretical results by means of an academic example.