🤖 AI Summary
This paper addresses the existence and computational tractability of market equilibria for heterogeneous agents with integer network flow capacity constraints, where coalition formation and path selection are interdependent. We propose an incentive-compatible edge-pricing mechanism that—novelty—integrates combinatorial auction theory with integer network flow optimization, establishing sufficient conditions for equilibrium existence and polynomial-time computability under topological and preference constraints. We prove that the utility-optimal equilibrium under this mechanism coincides with the VCG outcome. The framework is extended to multi-period settings and general networks via a preference-aware, path-level discriminatory pricing scheme. Our core contributions are threefold: (i) theoretical guarantee of equilibrium existence and efficient computability for integer flow allocations; (ii) methodological innovation through the cross-fertilization of combinatorial auctions and network flow theory; and (iii) a practical paradigm for fair and efficient allocation of scarce network resources in sharing economies.
📝 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 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.
