Matching with Choice Correspondences: Persistence and Acyclicity

Abstract

We study stable matching when agents are described by choice correspondences rather than preferences. For many-to-many markets, we introduce individually rational persistence (IRP) and show that substitutability (SUB) and IRP give a stable matching, through a simple algorithm with no proposing side. For one-to-one markets, SUB and binary acyclicity (BA) give a stable matching. Combining the two, SUB with IRP on firms and BA on workers gives a stable many-to-one matching. Because IRP and BA are each independent of irrelevance of rejected contracts (IRC), our conditions offer an alternative to path independence.