Optimal Transport Model Solves Heterogeneous Congestion Games

In a new preprint from UC Berkeley researchers Pan-Yang Su, Negar Mehr, and Shankar Sastry, a novel nonatomic congestion game framework tackles a long-standing problem: how to model agents with heterogeneous destination valuations who share congested network resources. Unlike prior models that either ignore diverse preferences or simplify aggregate congestion, this work introduces a measure space of agent valuations. Using Kantorovich duality from optimal transport theory, the authors derive finite-dimensional representations for both Nash equilibria and social optima, characterized by threshold vectors and dual potentials. These structures directly partition the valuation space, determining which destination each agent type chooses.

The 37-page paper (under review) includes 3 figures and is posted on arXiv (2607.03625). Its approach bridges game theory and optimal transport, offering a geometric lens on congestion dynamics. The framework applies directly to emerging urban systems like advanced air mobility, electric vehicle charging networks, and shared mobility services. By enabling efficient computation of equilibria and social optima, the work could lead to better pricing and routing algorithms for real-world infrastructure. The authors' method also provides a tractable way to handle large-scale agent heterogeneity without losing analytical precision.