General Matching Games

TL;DR

This paper extends the matching game model to more general market settings, providing conditions for stable outcomes and efficient computation methods, thus broadening its applicability.

Contribution

It introduces a generalized framework for matching games, including one-to-many markets and roommates models, with new conditions for stability and algorithms for outcome computation.

Findings

Core stable and renegotiation-proof outcomes exist under specified frameworks.

The paper provides efficient algorithms for computing these outcomes.

The model encompasses most one-to-many matching markets and roommates models.

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.