Market Design for Capacity Sharing in Networks
Saurabh Amin, Patrick Jaillet, Haripriya Pulyassary, Manxi Wu
TL;DR
The paper tackles designing market mechanisms for capacity sharing on networks where agents form coalitions to use one unit of capacity along a route. It develops a framework linking edge pricing to coalition formation via a network-flow model, proving that a market equilibrium exists and can be computed in polynomial time when the network is series-parallel and capacity-sharing disutilities are homogeneous; this equilibrium aligns with the VCG mechanism and thus is strategyproof under centralized implementation. The authors connect equilibrium existence to the zero integrality gap of a social-welfare linear program and provide a two-step algorithm combining greedy flow computation with Walrasian-equilibrium allocation in an auxiliary economy. They extend the static model to multi-period settings, general networks using path-based pricing, and branch-and-price methods for multi-population settings, offering practical approaches for carpooling and on-demand logistics while highlighting conditions under which equilibrium may fail and how to recover it. Overall, the work delivers a principled market-design approach for congestion-aware resource sharing with strong theoretical guarantees and practical extensions.
Abstract
We study a market mechanism that sets edge prices to incentivize strategic agents to efficiently share limited network capacity. In this market, agents form coalitions, with each coalition sharing a unit capacity of a selected route and making payments to cover edge prices. Our focus is on the existence and computation of market equilibrium, where challenges arise from the interdependence between coalition formation among strategic agents with heterogeneous preferences and route selection that induces a network flow under integral capacity constraints. To address this interplay between coalition formation and network capacity utilization, we introduce a novel approach based on combinatorial auction theory and network flow theory. We establish sufficient conditions on the network topology and agents' preferences that guarantee both the existence and polynomial-time computation of a market equilibrium. Additionally, we identify a particular market equilibrium that maximizes utilities for all agents and the outcome is equivalent to the classical Vickrey-Clarke-Groves mechanism. Furthermore, we extend our results to multi-period settings and general networks, showing that when the sufficient conditions are not met, an equilibrium may still exist but requires more complex, path-based pricing mechanisms that set differentiated prices based on agents' preference parameters.