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Matching in Networks: Structure of the Set of Stable Allocations

Author

Listed:
  • 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)

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.

Suggested Citation

  • Alejandra Garces & Alejandro Neme & Eliana Pepa Risma, 2024. "Matching in Networks: Structure of the Set of Stable Allocations," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 26(04), pages 1-23, December.
    • Handle: RePEc:wsi:igtrxx:v:26:y:2024:i:04:n:s0219198924500105
    DOI: 10.1142/S0219198924500105
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