arXiv subjects

Jorge Oviedo

Publications and source records attributed to Jorge Oviedo.

15 recordsLinked to original sources

arXiv2026

A polyhedral characterization of worker-quasi-stable matchings

We provide the first polyhedral characterization of worker-quasi-stable matchings in the classical one-to-one matching model. By modifying the classical stability constraints, we introduce a convex polytope and prove that it is integral. Consequently, its extreme points coincide exactly with the incidence vectors of worker-quasi-stable matchings, demonstrating that worker-quasi-stability preserves the geometric tractability of standard stability.

econ.TH↗

arXiv2026

A characterization of the von Neumann and Morgenstern stable set in matching markets

This paper studies the structure and computation of von Neumann-Morgenstern (vNM) stable sets in one-to-one matching markets. While pairwise stability and corewise stability coincide under strict preferences and provide a well-understood benchmark, vNM stability is defined through dominance relations among sets of matchings and remains considerably more difficult to characterize. A key contribution of the paper is a generalization of the classical Decomposition Lemma. We show that the structural decomposition traditionally used to compare stable matchings extends to any pair of matchings belonging to the same internally stable set. This result reveals a previously unexplored connection between internal stability and the cycle structure underlying matching markets. Building on this characterization, we identify the relationships that are relevant for dominance-based stability and derive a reduced environment that concentrates all undominated outcomes. Our main result shows that the vNM stable set is unique and admits a simple characterization in terms of the core of this reduced environment. The characterization provides both structural insight and a constructive procedure for computing the vNM stable set using standard matching theoretic tools.

econ.TH↗

arXiv2026

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

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.

econ.TH↗

arXiv2025

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

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.

econ.TH↗

arXiv2024

Dynamic matching games: stationary equilibria under varying commitments

This paper examines equilibria in dynamic two-sided matching games, extending Gale and Shapley's foundational model to a non-cooperative, decentralized, and dynamic framework. We focus on markets where agents have utility functions and commitments vary. Specifically, we analyze a dynamic matching game in which firms make offers to workers in each period, considering three types of commitment: (i) no commitment from either side, (ii) firms' commitment, and (iii) workers' commitment. Our results demonstrate that stable matchings can be supported as stationary equilibria under different commitment scenarios, depending on the strategies adopted by firms and workers. Furthermore, we identify key conditions, such as discount factors, that influence agents' decisions to switch partners, thereby shaping equilibrium outcomes.

econ.TH↗

arXiv2024

Quasi-stability notions in two-sided matching models

This paper presents weakened notions of corewise stability and setwise stability for matching markets where agents have substitutable choice functions. We introduce the concepts of worker-quasi-core, firm-quasi-core, and worker-quasisetwise stability. We also examine their relationship to established notions in the literature, such as worker-quasi and firm-quasi stability in both many-to-one and many-to-many markets.

econ.TH↗

arXiv2024

Counting steps for re-stabilization in a labor matching market

We study a one-to-one labor matching market. If a worker considers resigning from her current job to obtain a better one, how long does it take for this worker to actually get it? We present an algorithm that models this situation as a re-stabilization process involving a vacancy chain. Each step of the algorithm is a link of such a chain. We show that the length of this vacancy chain, which can be interpreted as the time the worker has to wait for her new job, is intimately connected with the lattice structure of the set of stable matchings of the market. Namely, this length can be computed by considering the cardinalities of cycles in preferences derived from the initial and final stable matchings involved.

econ.TH↗

arXiv2024

Nash implementation in a many-to-one matching market

In a many-to-one matching market, we analyze the matching game induced by a stable rule when firms' choice function satisfy substitutability. We show that any stable rule implements the individually rational correspondence in Nash equilibrium when both sides of the market play strategically. Moreover, when only workers play strategically and firms' choice functions satisfy the law of aggregate demand, we show that the firm-optimal stable rule implements the stable correspondence in Nash equilibrium.

econ.TH↗

arXiv2022

General Manipulability Theorem for a Matching Model

In a many-to-many matching model in which agents' preferences satisfy substitutability and the law of aggregate demand, we proof the General Manipulability Theorem. We result generalizes the presented in Sotomayor (1996 and 2012) for the many-to-one model. In addition, we show General Manipulability Theorem fail when agents' preferences satisfy only substitutability.

econ.TH↗

arXiv2022

The lattice of envy-free many-to-many matchings with contracts

We study envy-free allocations in a many-to-many matching model with contracts in which agents on one side of the market (doctors) are endowed with substitutable choice functions and agents on the other side of the market (hospitals) are endowed with responsive preferences. Envy-freeness is a weakening of stability that allows blocking contracts involving a hospital with a vacant position and a doctor that does not envy any of the doctors that the hospital currently employs. We show that the set of envy-free allocations has a lattice structure. Furthermore, we define a Tarski operator on this lattice and use it to model a vacancy chain dynamic process by which, starting from any envy-free allocation, a stable one is reached.

econ.TH↗

arXiv2022

Core and stability notions in many-to-one matching markets with indifferences

In a many-to-one matchingmodel with responsive preferences in which indifferences are allowed, we study three notions of core, three notions of stability, and their relationships. We show that (i) the core contains the stable set, (ii) the strong core coincides with the strongly stable set, and (iii) the super core coincides with the super stable set. We also show how the core and the strong core in markets with indifferences relate to the stable matchings of their associated tie-breaking strict markets.

econ.TH↗

arXiv2022

The lattice of worker-quasi-stable matchings

In a many-to-one matching model in which firms' preferences satisfy substitutability, we study the set of worker-quasi-stable matchings. Worker-quasi-stability is a relaxation of stability that allows blocking pairs involving a firm and an unemployed worker. We show that this set has a lattice structure and define a Tarski operator on this lattice that models a re-equilibration process and has the set of stable matchings as its fixed points.

econ.TH↗

arXiv2022

Cycles to compute the full set of many-to-many stable matchings

In a many-to-many matching model in which agents' preferences satisfy substitutability and the law of aggregate demand, we present an algorithm to compute the full set of stable matchings. This algorithm relies on the idea of "cycles in preferences" and generalizes the algorithm presented in Roth and Sotomayor (1990) for the one-to-one model.

econ.TH↗

arXiv2020

Lattice structure of the random stable set in many-to-many matching market

For a many-to-many matching market, we study the lattice structure of the set of random stable matchings. We define a partial order on the random stable set and present two intuitive binary operations to compute the least upper bound and the greatest lower bound for each side of the matching market. Then, we prove that with these binary operations the set of random stable matchings forms two dual lattices.

econ.TH↗

arXiv2020

On the many-to-one strongly stable fractional matching set

For a many-to-one matching market where firms have strict and $\boldsymbol{q}$-responsive preferences, we give a characterization of the set of strongly stable fractional matchings as the union of the convex hull of all connected sets of stable matchings. Also, we prove that a strongly stable fractional matching is represented as a convex combination of stable matchings that are ordered in the common preferences of all firms.

econ.TH↗