Pseudo-Substitutability: A Maximal Domain for Pairwise Stability in Matching Markets with Contracts

TL;DR

This paper introduces pseudo-substitutable preferences, a domain that extends classical substitutability to ensure the existence of pairwise stable allocations in matching markets with contracts.

Contribution

It defines a new preference domain that guarantees stability and is maximal among those extending classical substitutability.

Findings

Pseudo-substitutable preferences guarantee pairwise stability.

The domain strictly extends classical substitutability.

Pseudo-substitutable domain is maximal among stability-guaranteeing domains.

Abstract

We study the existence of pairwise stable allocations in matching markets with contracts and propose a domain restriction that guarantees their existence. Specifically, we define pseudo-substitutable preferences, a domain that strictly extends the classical notion of substitutability while still preserving the existence of pairwise stable allocations. This domain accommodates limited complementarities among contracts while retaining enough structure to preserve the key stability properties of substitutable preferences. Moreover, we show that, among all preference domains that contain the classical substitutable domain and guarantee the existence of pairwise stable allocations, the pseudo-substitutable domain is maximal. Our results establish that pairwise stability extends well beyond the classical substitutable domain.