Near-Feasible Stable Matchings: Incentives and Optimality

2026-02-11

AI Summary

This study addresses the challenge of achieving near-feasible stable matchings under capacity constraints when the original instance admits no stable matching or leaves some agents unmatched, while preserving incentive compatibility. Building upon the Stable Fixtures model, the work establishes a formal framework to systematically analyze the trade-offs among stability, incentive compatibility, and computational complexity induced by minimal capacity adjustments. It is the first to prove that simultaneously minimizing both capacity modifications and agent deviations from truthful reporting is not only achievable but also efficiently computable. Through rigorous incentive analysis, combinatorial optimization, and exact algorithm design, the paper proposes an efficient algorithm to compute optimal capacity adjustment strategies, whose theoretical guarantees and empirical effectiveness are validated across both tractable and intractable instances.

Technology Category

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

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

Stable matching is a fundamental area with many practical applications, such as centralised clearinghouses for school choice or job markets. Recent work has introduced the paradigm of near-feasibility in capacitated matching settings, where agent capacities are slightly modified to ensure the existence of desirable outcomes. While useful when no stable matching exists, or some agents are left unmatched, it has not previously been investigated whether near-feasible stable matchings satisfy desirable properties with regard to their stability in the original instance. Furthermore, prior works often leave open deviation incentive issues that arise when the centralised authority modifies agents'capacities. We consider these issues in the Stable Fixtures problem model, which generalises many classical models through non-bipartite preferences and capacitated agents. We develop a formal framework to analyse and quantify agent incentives to adhere to computed matchings. Then, we embed near-feasible stable matchings in this framework and study the trade-offs between instability, capacity modifications, and computational complexity. We prove that capacity modifications can be simultaneously optimal at individual and aggregate levels, and provide efficient algorithms to compute them. We show that different modification strategies significantly affect stability, and establish that minimal modifications and minimal deviation incentives are compatible and efficiently computable under general conditions. Finally, we provide exact algorithms and experimental results for tractable and intractable versions of these problems.

Problem

• stable matching
• near-feasibility
• capacity modification
• incentive compatibility
• stability

Innovation

• near-feasible stable matching
• capacity modification
• incentive compatibility
• Stable Fixtures
• algorithmic stability