Distributed Algorithm for Robust Wardrop Equilibrium in Uncertain Aggregative Congestion Games
2026-06-01 • Computer Science and Game Theory
Computer Science and Game Theory
AI summaryⓘ
The authors study a type of game where many players share resources but face uncertain limits on usage, like in traffic or network congestion. They transform the problem to make it simpler and develop an algorithm that each player can run independently to find a stable solution that works even in worst-case uncertainty. They prove their method converges reliably and explain how this solution relates to other equilibrium concepts that consider more complex player interactions. They also test their approach using electric vehicle charging scenarios to show it works in practice.
aggregative congestion gamesuncertain coupling constraintsrobust generalized Wardrop equilibriumrobust optimizationprojected primal-dual algorithmdynamic trackingsingular perturbation theoryLaSalle's invariance principlerobust generalized Nash equilibriumelectric vehicle charging control
Authors
Huan Peng, Guanpu Chen, Giuseppe Belgioioso, Karl Henrik Johansson
Abstract
This paper considers a class of aggregative congestion games with uncertain coupling constraints, and devises a distributed algorithm to seek the robust generalized Wardrop equilibrium (RGWE) under worst-case uncertainty. Utilizing robust optimization theory, we reformulate the original aggregative congestion game with uncertainty into a tractable and deterministic augmented problem. Building upon this reformulation, we design a fully distributed algorithm to seek the RGWE by integrating a projected primal-dual scheme and a dynamic tracking technique. The convergence of the proposed algorithm is rigorously guaranteed via singular perturbation theory and LaSalle's invariance principle. Furthermore, we explicitly characterize the relationship between the obtained RGWE and the robust generalized Nash equilibrium, as the latter captures full strategic interactions. Finally, numerical simulations on the charging control of plug-in electric vehicles corroborate our theoretical findings.