A decomposition from a many-to-one matching market with path-independent choice functions to a one-to-one matching market

Pablo Neme; Jorge Oviedo

Home/Archive/arXiv

arXiv · 2411.00564

A decomposition from a many-to-one matching market with path-independent choice functions to a one-to-one matching market

Pablo Neme·Jorge Oviedo

View original source ↗Read source document ↗Export metadata ↓

Abstract

For a many-to-one market where firms are endowed with path-independent choice functions, based on the Aizerman-Malishevski decomposition, we define an associated one-to-one market. Given that the usual notion of stability for a one-to-one market does not fit well for this associated one-to-one market, we introduce a new notion of stability. This notion allows us to establish an isomorphism between the set of stable matchings in the many-to-one market and the matchings in an associated one-to-one market that meet this new stability criterion. Furthermore, we present an adaptation of the well-known deferred acceptance algorithm to compute a matching that satisfies this new notion of stability for the associated one-to-one market. Finally, as a byproduct of our isomorphism, we prove an adapted version of the so-called Rural Hospital Theorem.

Explore related subjects

econ.TH cs.GT

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Pablo Neme, Jorge Oviedo. 2025-05-15. A decomposition from a many-to-one matching market with path-independent choice functions to a one-to-one matching market. https://arxiv.org/abs/2411.00564

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Log-concave functions and transformations thereof

I summarize Bagnoli and Bergstrom (2005)'s review on log-concave functions, make several corrections, and augment the discussion with further results that can be useful in establishing monotone hazard rates. I also provide an application to monopoly pricing, where log-concavity of the demand curve implies strict concavity of the revenue function in quantity.

econ.TH↗

arXiv2026

Audit the Auditors: Commitment versus Professional Judgment

This paper provides a theoretical framework to evaluate the trade-off between the self-regulated peer review system and independent government inspection (PCAOB) in the auditing profession. We model the peer review system as a Judgment Regime, where a stakeholder utilizes professional expertise, captured as a private signal, to make ex-post decisions on verifying audit failures. In contrast, PCAOB inspection is modeled as a Commitment Regime, where the stakeholder lacks private information but can commit ex-ante to a predetermined level of verification. We find that the Judgment Regime benefits from a resource-allocation effect and a deterrence effect driven by informed verification, whereas the Commitment Regime deters audit failures through the first-mover advantage of ex-ante commitment. Our analysis demonstrates that the stakeholder prefers the peer review system if and only if the private signal is sufficiently informative. Furthermore, comparative statics reveal that higher verification costs or stronger audit incentives shift the stakeholder's preference toward PCAOB inspection.

econ.TH↗

arXiv2026

Reputation, Disclosure, and the Scope of Entry

This paper studies how learning about an incumbent affects the scope of entry when competitive responses use resources shared across markets. An entrant chooses whether to launch in neither, one, or both of two markets. Entry into the second market reduces the incumbent's cost-reducing response in the first and can make one-market entry unattractive. The entrant learns about the incumbent's capability from a record of its response to an earlier rival. More frequent publication encourages a less capable incumbent to imitate a more capable one. An observed response then becomes less informative, and entry after that record expands. We compare publication of conduct with a public audit of capability. For an open set of parameters with uniform setup costs, full publication maximizes total surplus within the specified policy class when publication costs are low. Removing the interaction between response costs across markets reverses this choice, while preserving all early and singleton-market payoffs. A capability audit is dominated in both economies. Expected entry scope is constant across the considered policies within each technology, although productive investment and the allocation of entry change.

econ.TH↗