Matching in Networks: Structure of the Set of Stable Allocations

Author:

Garces Alejandra1ORCID,Neme Alejandro2ORCID,Pepa Risma Eliana2ORCID

Affiliation:

1. Universidad Nacional de San Juan, Av. Ignacio de la Roza 590 (O), 5402 San Juan, Argentina

2. Instituto de Matemática Aplicada San Luis, Universidad Nacional de San Luis and CONICET, Ejército de los Andes 950, 5700 San Luis, Argentina

Abstract

Matching models with contracts have been extensively studied in the last years as a generalization of the classical matching theory. Matching in networks is an even more general model in which firms trade goods via bilateral contracts constituting a supply chain. Hatfield and Kominers ([2012] Matching in networks with bilateral contracts, Am. Econ. J., Microecon. 4(1), 176–208, doi:10.1257/mic.4.1.176) showed that a natural substitutability condition characterizes the maximal domain of firm preferences for which the existence of stable allocations is guaranteed in such a model, if the set of all existent contracts is acyclic. Moreover, they asserted that these conditions are sufficient to obtain a suitable lattice structure for the set of all stable allocations. In this paper, we exhibit an inconsistency in the last point through an example, and introduce an additional condition over firm preferences that allows to recover an appropriate lattice structure.

Funder

UNSL

Consejo Nacional de Investigaciones Científicas y Técnicas

Agencia Nacional de Promoción Científica y Tecnológica

Publisher

World Scientific Pub Co Pte Ltd

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