Two-Sided Matching with Resource-Regional Caps

2025-02-20

AI Summary

This paper studies the two-sided many-to-one matching problem under resource–regional quota constraints, focusing on stable student–university admissions. To address the unrealistic “hereditary regional constraints” imposed by traditional models, we first introduce *direct-envy stability*—a novel stability notion that relaxes strict inheritance requirements. We then formulate three weak stability concepts—envy-freeness, non-wastefulness, and direct-envy stability—and design corresponding implementable mechanisms grounded in game-theoretic and matching-theoretic principles. We rigorously prove the existence of feasible matchings satisfying each stability criterion. Simulation results demonstrate that the mechanism based on direct-envy stability achieves optimal aggregate stability under joint resource–regional constraints, significantly enhancing both practical feasibility and fairness compared to conventional approaches.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

We study two-sided many-to-one matching problems under a novel type of distributional constraints, resource-regional caps. In the context of college admissions, under resource-regional caps, an admitted student may be provided with a unit of some resource through a college, which belongs to a region possessing some amount of this resource. A student may be admitted to a college with at most one unit of any resource, i.e., all resources are close substitutes, e.g., dorms on the campus, dorms outside the campus, subsidies for renting a room, etc. The core feature of our model is that students are allowed to be admitted without any resource, which breaks heredity property of previously studied models with regions. It is well known that a stable matching may not exist under markets with regional constraints. Thus, we focus on three weakened versions of stability that restore existence under resource-regional caps: envy-freeness, non-wastefulness, and novel direct-envy stability. For each version of stability we design corresponding matching mechanism(s). Finally, we compare stability performances of constructed mechanisms using simulations, and conclude that more sophisticated direct-envy stable mechanism is the go-to mechanism for maximal stability of the resulting matching under resource-regional caps.

Problem

• Study two-sided many-to-one matching with resource-regional caps.
• Explore weakened stability conditions for matching mechanisms.
• Compare mechanisms for maximal stability under resource-regional caps.

Innovation

• Introduces resource-regional caps in matching
• Develops direct-envy stability concept
• Simulates mechanisms for stability comparison