Pseudo-Substitutability: A Maximal Domain for Pairwise Stability in Matching Markets with Contracts
Nadia Guiñazú, Noelia Juarez, Paola Manasero, Pablo Neme, Jorge Oviedo
TLDR
This paper introduces pseudo-substitutable preferences, a maximal domain that extends classical substitutability to guarantee pairwise stability in contract markets.
Key contributions
- Introduces pseudo-substitutable preferences for matching markets with contracts.
- This new domain strictly extends the classical notion of substitutability.
- Guarantees the existence of pairwise stable allocations, even with limited complementarities.
- Proves pseudo-substitutability is a maximal domain for this stability guarantee.
Why it matters
This paper expands stable matching theory, demonstrating pairwise stability in more complex markets with contracts. It enables realistic modeling of scenarios with limited complementarities, significantly extending stable matching applicability.
Original 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.
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