arXiv subjects

Pablo Neme

Publications and source records attributed to Pablo Neme.

14 recordsLinked to original sources

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

Sharing the proceeds from a hierarchical venture when agents have needs

We consider a setting in which a set of agents are hierarchically organized for a joint venture. They each generate revenues for the joint venture and have individual needs to cover. The aim is to distribute aggregate revenues appropriately. We characterize a family of need-adjusted geometric rules where the net revenue (after covering needs) "bubbles up" in the hierarchy, as well as a need-adjusted serial rule in which the net revenue is equally shared among each agent and his predecessors in the hierarchy.

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

Coalitional stability under myopic expectations and externalities

We study coalition formation problems in the presence of externalities, focusing on settings where agents exhibit myopic expectations, that is, they evaluate potential deviations based solely on the immediate outcome, assuming no further reactions or reorganization by others. First, we establish a sufficient condition for the non-emptiness of both the core and the stable set. In the case of the core, our condition for ensuring non-emptiness also provides a characterization of all core partitions. We then turn our attention to problems with order-preserving preferences. Under our sufficient condition, the core and the stable set not only exist but also coincide, and convergence to a stable outcome is guaranteed. Furthermore, using the notion of absorbing set, we draw a connection between problems with order-preserving preferences and those without externalities. This allows us to lift known core non-emptiness results from the latter setting to the former, thereby establishing a novel bridge between these two classes of problems.

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

Mechanisms for a dynamic many-to-many school choice problem

We examine the problem of assigning teachers to public schools over time when teachers have tenured positions and can work simultaneously in multiple schools. To do this, we investigate a dynamic many-to-many school choice problem where public schools have priorities over teachers and teachers hold path-independent choice functions selecting subsets of schools. We introduce a new concept of dynamic stability that recognizes the tenured positions of teachers and we prove that a dynamically stable matching always exists. We propose the Tenure-Respecting Deferred Acceptance (TRDA) mechanism, which produces a dynamically stable matching that is constrained-efficient within the class of dynamically stable matchings and minimizes unjustified claims. To improve efficiency beyond this class, we also propose the Tenure-Respecting Efficiency-Adjusted Deferred Acceptance (TREADA) mechanism, an adaptation of the Efficiency-Adjusted Deferred Acceptance mechanism to our dynamic context. We demonstrate that the outcome of the TREADA mechanism Pareto-dominates any dynamically stable matching and achieves efficiency when all teachers consent. Additionally, we examine the issue of manipulability, showing that although the TRDA and TREADA mechanisms can be manipulated, they remain non-obviously dynamically manipulable under specific conditions on schools' priorities.

econ.TH↗

arXiv2024

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

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↗

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↗

arXiv2021

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↗

arXiv2021

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↗

arXiv2020

A characterization of absorbing sets in coalition formation games

Given a standard myopic dynamic process among coalition structures, an absorbing set is a minimal collection of such structures that is never left once entered through that process. Absorbing sets are an important solution concept in coalition formation games, but they have drawbacks: they can be large and hard to obtain. In this paper, we characterize an absorbing set in terms of a collection consisting of a small number of sets of coalitions that we refer to as a "reduced form" of a game. We apply our characterization to study convergence to stability in several economic environments.

econ.TH↗