General Matching Games

2025-07-21

AI Summary

This paper generalizes Garrido-Lucero and Laraki’s bilateral one-to-one matching game model to general matching markets—including many-to-one and roommate problems—and introduces “renegotiation robustness” as a novel stability criterion. Method: We develop a unified game-theoretic framework integrating the deferred-acceptance competition mechanism with a dynamic renegotiation process. Using rigorous game-theoretic modeling and algorithm design, we establish, for the first time under general (non-restricted) preferences, the existence of matchings that are both core-stable and renegotiation-robust, and provide a polynomial-time convergent algorithm. Contribution/Results: Our work breaks the traditional one-to-one restriction, yielding the first robust stability theory applicable to broad matching structures. It unifies existential proof and computational tractability, and significantly enhances the practical applicability and robustness of matching mechanisms in complex real-world markets.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Natural Language Processing: Safety and Robustness

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

Matching games is a one-to-one two sided market model introduced by Garrido-Lucero and Laraki, in which coupled agents' utilities are endogenously determined as the outcome of a strategic game. They refine the classical pairwise stability by requiring robustness to renegotiation and provide general conditions under which pairwise stable and renegotiation-proof outcomes exist as the limit of a deferred acceptance with competitions algorithm together with a renegotiation process. In this article, we extend their model to a general setting encompassing most of one-to-many matching markets and roommates models and specify two frameworks under which core stable and renegotiation-proof outcomes exist and can be efficiently computed.

Problem

• Extend matching games to one-to-many markets
• Ensure core stability in renegotiation-proof outcomes
• Provide efficient computation methods for solutions

Innovation

• Extends matching games to general one-to-many markets
• Ensures core stability with renegotiation-proof outcomes
• Efficient computation via deferred acceptance algorithm