Congestion Games with Heterogeneous Valuations: An Optimal Transport Approach

2026-07-03

AI Summary

This study addresses the challenge that existing congestion game models struggle to simultaneously capture agents’ heterogeneous destination preferences and system-level congestion externalities. The authors propose a novel nonatomic congestion game framework in which heterogeneous valuations are modeled as a measure space, and for the first time employ Kantorovich duality theory to analyze Nash equilibria and social optima. By integrating optimal transport, measure theory, and variational analysis, they demonstrate that the equilibrium structure can be precisely characterized by a finite-dimensional threshold vector and a dual potential function, yielding an explicit partition of the valuation space into decision regions. This work establishes a finite-dimensional, computationally tractable representation of congestion games with heterogeneous preferences, offering a new paradigm for resource allocation in applications such as urban air mobility and electric vehicle charging.

Abstract

In emerging urban mobility and logistics applications, such as advanced air mobility, electric vehicle charging, and shared service systems, agents with heterogeneous valuations choose among multiple destinations while sharing congested network resources. However, existing congestion game and resource allocation models do not simultaneously capture heterogeneous destination preferences and aggregate congestion externalities. We introduce a new nonatomic congestion game framework in which agents are endowed with heterogeneous destination valuations modeled by a measure space. We characterize Nash equilibria and social optima in this setting and show that both admit finite-dimensional representations in terms of threshold vectors and dual potentials. These structures induce a partition of the valuation space that determines agents' destination choices. Our analysis leverages Kantorovich duality from optimal transport theory and provides a new geometric perspective on congestion games with heterogeneous valuations.

Problem

• congestion games
• heterogeneous valuations
• resource allocation
• congestion externalities
• destination preferences

Innovation

• congestion games
• heterogeneous valuations
• optimal transport
• Kantorovich duality
• nonatomic games