Matching in Networks: Structure of the Set of Stable Allocations

Alejandra Garces (), Alejandro Neme () and Eliana Pepa Risma
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Alejandra Garces: Universidad Nacional de San Juan, Av. Ignacio de la Roza 590 (O), 5402 San Juan, Argentina
Alejandro Neme: Instituto de Matemática Aplicada San Luis, Universidad Nacional de San Luis and CONICET, Ejército de los Andes 950, 5700 San Luis, Argentina
Eliana Pepa Risma: Instituto de Matemática Aplicada San Luis, Universidad Nacional de San Luis and CONICET, Ejército de los Andes 950, 5700 San Luis, Argentina

International Game Theory Review (IGTR), 2024, vol. 26, issue 04, 1-23

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.

Keywords: Matching; contracts; networks; market design (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0219198924500105

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