Facilitating Matches on Allocation Platforms

2025-08-24

AI Summary

This paper addresses the problem of enhancing social welfare in two-sided matching platforms without degrading existing high-quality matches, while respecting budget and resource constraints. It proposes a selective constraint-relaxation mechanism wherein only a subset of agents—e.g., those with overly restrictive preferences or eligibility criteria—are guided to moderately loosen their constraints. To ensure fairness and efficiency, the authors introduce a hierarchical participation guarantee framework and a customizable social welfare objective function. They formulate the problem as a combinatorial optimization model and design polynomial-time algorithms applicable to both one-to-one and many-to-one matching settings. Extensive experiments on three real-world datasets demonstrate that the proposed approach significantly improves matching efficiency and aggregate social welfare. Quantitative analysis further reveals how different participation guarantees affect system performance, empirically validating the method’s effectiveness and practical applicability.

Technology Category

• Multiagent Systems: Mechanism Design
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

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

Abstract

We consider a setting where goods are allocated to agents by way of an allocation platform (e.g., a matching platform). An ``allocation facilitator'' aims to increase the overall utility/social-good of the allocation by encouraging (some of the) agents to relax (some of) their restrictions. At the same time, the advice must not hurt agents who would otherwise be better off. Additionally, the facilitator may be constrained by a ``bound'' (a.k.a. `budget'), limiting the number and/or type of restrictions it may seek to relax. We consider the facilitator's optimization problem of choosing an optimal set of restrictions to request to relax under the aforementioned constraints. Our contributions are three-fold: (i) We provide a formal definition of the problem, including the participation guarantees to which the facilitator should adhere. We define a hierarchy of participation guarantees and also consider several social-good functions. (ii) We provide polynomial algorithms for solving various versions of the associated optimization problems, including one-to-one and many-to-one allocation settings. (iii) We demonstrate the benefits of such facilitation and relaxation, and the implications of the different participation guarantees, using extensive experimentation on three real-world datasets.

Problem

• Optimizing restriction relaxation to improve allocation platform utility
• Ensuring advice does not harm agents' original benefits
• Selecting optimal restrictions to relax under budget constraints

Innovation

• Formal problem definition with participation guarantees hierarchy
• Polynomial algorithms for one-to-one and many-to-one allocation
• Extensive experimentation on three real-world datasets