Quasi-stability notions in two-sided matching models

TL;DR

This paper introduces weakened stability concepts like worker-quasi-core and firm-quasi-core for matching markets with substitutable choice functions, analyzing their relationships to existing stability notions.

Contribution

It proposes new quasi-stability notions in two-sided matching models and explores their connections to established stability concepts.

Findings

Defined worker-quasi-core, firm-quasi-core, and worker-quasi-setwise stability.

Analyzed relationships between new and existing stability notions.

Extended concepts to many-to-one and many-to-many markets.

Abstract

This paper presents weakened notions of corewise stability and setwise stability for matching markets where agents have substitutable choice functions. We introduce the concepts of worker-quasi-core, firm-quasi-core, and worker-quasisetwise stability. We also examine their relationship to established notions in the literature, such as worker-quasi and firm-quasi stability in both many-to-one and many-to-many markets.