On inverse aggregate network assignment games

Abstract

To design platforms for multi-operator mobility markets coordinating their operations or infrastructure to support them, models are needed to understand the behavior of these operators and travelers in a shared network. Assignment games can prove useful, but operationalizing them requires adopting a more generalized aggregate assignment game framework that allows for identification and estimation. We extend such a framework to aggregate network assignment games, proposing a path-based formulation and a PURC-based formulation along with solution algorithms. An inverse optimization model is proposed for the link-based formulation. It is solved by a quadratic program that separates into a buyer block, which retains the node potentials and imposes every observed zero-flow cell, and a seller block. This estimator, introduced in the literature for uncapacitated route choice, is extended here to a capacitated two-sided market, with rationing prices supported on observed binding links and operator supply scales estimated by group. Computational tests with a toy network demonstrate the economic value of these models. A large-scale Long Island Rail Road network example (897 nodes, 671 census tracts, 123 LIRR stations, 8,320 directed links) is calibrated to 2026 fares, timetabled seat supply and National Transit Database operating costs. With 10-50% of links sampled, the misspecified inverse model fits oracle link flows with R^2>=96%. Held-out link error falls from 29% to 19%, correlations with the true rationing prices rise from 49% to 75%, and social optimal gross surplus is recovered within 6%. Deadweight loss is overestimated by 10-17%. Ablation tests show that ignoring the inactive cells more than doubles the held-out error and, at 30-50% sampling, roughly halves the correlation of the pricing wedge, while ignoring the rationing prices degrades every metric.