Core and stability notions in many-to-one matching markets with indifferences

TL;DR

This paper explores core and stability concepts in many-to-one matching markets with indifferences, establishing relationships among various core and stability notions and their connections to tie-breaking models.

Contribution

It introduces and compares multiple core and stability notions in markets with indifferences, clarifying their relationships and links to strict market models.

Findings

Core contains the stable set.

Strong core equals strongly stable set.

Super core equals super stable set.

Abstract

In a many-to-one matchingmodel with responsive preferences in which indifferences are allowed, we study three notions of core, three notions of stability, and their relationships. We show that (i) the core contains the stable set, (ii) the strong core coincides with the strongly stable set, and (iii) the super core coincides with the super stable set. We also show how the core and the strong core in markets with indifferences relate to the stable matchings of their associated tie-breaking strict markets.