Congestion Games with Heterogeneous Valuations: An Optimal Transport Approach

What the math gives to ML

The paper provides an explicit way to route heterogeneous agents through congestible alternatives: for a fixed congestion-price vector, the valuation space is partitioned into measurable destination regions by an argmax rule, with indifference boundaries negligible under absolute continuity. This suggests replacing uniform or purely heuristic load balancing in mixture-of-experts networks with a utility-aware congestion equilibrium, where each token has a vector of expert valuations and expert prices rise with batch load. The practical transfer is a hard or straight-through threshold router coupled to dual price updates, tested against top-k routing and standard auxiliary load-balancing losses at equal capacity and FLOPs.