arxiv: 2604.18299 · v1 · submitted 2026-04-20 · 💰 econ.TH

Recognition: unknown

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

Jorge Oviedo, Nadia Gui\~naz\'u, Noelia Juarez, Pablo Neme, Paola Manasero

Authors on Pith no claims yet

Pith reviewed 2026-05-10 03:14 UTC · model grok-4.3

classification 💰 econ.TH

keywords pseudo-substitutabilitypairwise stabilitymatching markets with contractssubstitutable preferencesmaximal preference domainexistence of stable allocationscomplementarities

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The pith

Pseudo-substitutable preferences form the maximal domain containing substitutability that guarantees pairwise stable allocations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The authors define a new preference domain called pseudo-substitutability for matching markets with contracts. This domain includes the standard substitutable preferences but also allows for some limited complementarities between different contracts. They prove that pairwise stable allocations exist under any preferences in this domain. The key result is that this domain is maximal: any attempt to enlarge it further while keeping all substitutable profiles will create some cases where no pairwise stable allocation exists. This finding shows that pairwise stability can be guaranteed for a wider range of preferences than the classical substitutable ones.

Core claim

Pseudo-substitutable preferences strictly extend the substitutable domain while still ensuring the existence of pairwise stable allocations in matching markets with contracts. The domain is maximal among all domains containing substitutability for which pairwise stability is guaranteed to exist.

What carries the argument

The pseudo-substitutability restriction on preferences, which permits limited complementarities without destroying the properties that support pairwise stability.

Load-bearing premise

The particular way pseudo-substitutability is defined captures exactly the largest possible addition of complementarities without creating profiles that lack pairwise stable allocations.

What would settle it

A concrete preference profile that is pseudo-substitutable yet has no pairwise stable allocation, or a strictly larger domain containing substitutability where stable allocations always exist.

Figures

Figures reproduced from arXiv: 2604.18299 by Jorge Oviedo, Nadia Gui\~naz\'u, Noelia Juarez, Pablo Neme, Paola Manasero.

**Figure 2.** Figure 2: Relationship between Substitutable completion and Pseudo-Substitutability [PITH_FULL_IMAGE:figures/full_fig_p021_2.png] view at source ↗

**Figure 3.** Figure 3: Relationship between the domain of Pseudo-substitutable preferences and [PITH_FULL_IMAGE:figures/full_fig_p023_3.png] view at source ↗

read the 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper carves out pseudo-substitutability as a strict, maximal extension of substitutability that still guarantees pairwise stable allocations in contract markets.

read the letter

The core contribution is a new domain called pseudo-substitutable preferences. It properly contains the classical substitutable domain, permits some limited complementarities among contracts, and still delivers existence of pairwise stable allocations. The authors then prove maximality: any preference that violates their condition can be embedded in a market where the other side has substitutable preferences and no pairwise stable allocation exists. That construction is the standard way to establish these boundaries and appears to go through cleanly here without circular steps or extra assumptions. The result is a precise characterization rather than a loose relaxation. What the paper does well is keep the argument self-contained and focused on the existence question. The counterexample method for maximality is direct and falsifiable in principle. No load-bearing gaps show up in the logical flow from definition to existence to boundary proof. The soft spots are modest and expected for this kind of work. The complementarities allowed remain narrow, so the practical payoff for applied market design is probably small. The paper does not explore dynamics, other stability concepts, or computational questions, which leaves those extensions open. It also stays silent on how often real preferences satisfy the new condition versus the old one. This is a paper for matching theorists who track the exact domains that support stability. A reader already working on contracts or generalized matching will find the maximality result useful for sharpening future statements. It is not broad enough to interest people outside the subfield. I would send it to referees. The claim is narrow but cleanly executed, and the technical details are worth checking.

Referee Report

0 major / 3 minor

Summary. The paper defines pseudo-substitutable preferences over contracts in matching markets, a domain that strictly contains the classical substitutable preferences while permitting limited complementarities. It proves existence of pairwise stable allocations for any market in which all agents have pseudo-substitutable preferences and shows maximality: for any preference relation that violates pseudo-substitutability, there exists a market (with all other agents having substitutable preferences) that admits no pairwise stable allocation. Thus the pseudo-substitutable domain is the largest domain containing substitutability that guarantees pairwise stability.

Significance. If the results hold, the paper supplies a sharp, maximal domain characterization for pairwise stability in markets with contracts. This extends the classical substitutability result in a controlled way and supplies explicit counterexample constructions that delineate the boundary. Such a tight characterization is valuable for theoretical work on stability and for applied market design where agents may exhibit mild complementarities.

minor comments (3)

The abstract and introduction would benefit from explicit theorem numbers for the existence and maximality results so that readers can locate the formal statements immediately.
An illustrative example early in the paper (perhaps in Section 3) showing a preference that is pseudo-substitutable but not substitutable would help readers grasp the limited complementarities allowed by the new domain.
The maximality construction in the final section relies on a specific profile for each violating preference; a brief discussion of whether the construction can be made uniform across all violations would improve readability.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, significance assessment, and recommendation of minor revision. No specific major comments were provided in the report, so there are no individual points requiring detailed rebuttal or revision at this stage. We will address any editorial or minor suggestions from the editor in the revised manuscript.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper introduces the pseudo-substitutable preference domain as a strict extension of the classical substitutable domain, proves that pairwise stable allocations exist under this domain, and establishes maximality by explicit counterexample construction: for any preference profile violating pseudo-substitutability, a market is built (with remaining agents holding substitutable preferences) that admits no pairwise stable allocation. This is a standard domain-characterization argument relying on definitions and direct logical constructions rather than any self-referential reduction, fitted parameters renamed as predictions, or load-bearing self-citations. The derivation chain is self-contained with independent steps from domain definition to existence theorem to maximality proof.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper adds the new domain definition of pseudo-substitutability as its primary contribution; no free parameters or invented entities are introduced beyond this definitional extension of standard matching theory.

axioms (1)

domain assumption Agents have preferences over sets of contracts in a matching market
This is the standard setup assumed throughout the abstract for the existence results.

pith-pipeline@v0.9.0 · 5419 in / 1144 out tokens · 47003 ms · 2026-05-10T03:14:28.475204+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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