Congestion Games with Heterogeneous Valuations: An Optimal Transport Approach

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.