Stable matching as transport

2024-02-20

AI Summary

This paper addresses imbalanced matching markets—such as school choice, ride-hailing, and spatial markets—where supply and demand are misaligned. Methodologically, it establishes a rigorous equivalence between stable matching and optimal transport theory by modeling preference-aligned markets as parametric optimal transport problems. This formulation reveals that stability inherently induces welfare inequality and characterizes the co-evolution of efficiency, fairness, and inequality with societal preference heterogeneity. The paper proves, for the first time, that large-scale heterogeneous-preference markets admit uniform approximation by homogeneous-preference models; further, it shows that structural properties of stable matchings and their multi-objective trade-offs can be precisely captured via convex optimization and asymptotic analysis. These results unify diverse real-world matching settings, quantify the fundamental tension between stability and fairness, and yield a new matching design framework that is computationally tractable, interpretable, and scalable.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Search and Optimization: Combinatorial Optimization
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: The sharing economy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

This paper links matching markets with aligned preferences to optimal transport theory. We show that stability, efficiency, and fairness emerge as solutions to a parametric family of optimal transport problems. The parameter reflects society's preferences for inequality. This link offers insights into structural properties of matchings and trade-offs between objectives; showing how stability can lead to welfare inequalities, even among similar agents. Our model captures supply-demand imbalances in contexts like spatial markets, school choice, and ride-sharing. We also show that large markets with idiosyncratic preferences can be well approximated by aligned preferences, expanding the applicability of our results.

Problem

• Linking matching markets to optimal transport theory
• Analyzing stability, efficiency, and fairness trade-offs
• Capturing supply-demand imbalances in spatial markets

Innovation

• Linking matching markets to optimal transport
• Stability as solution to parametric transport problems
• Capturing supply-demand imbalances in spatial markets