Networks Matching with Contract: The Set of Stable Allocations

ALEJANDRO NEME

Congreso; XLII Reunión anual de la Asociación Argentina de Economía Política; 2017

AAEP

Matching models with contracts have been extensively studied in the last decade 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. Previous literature on this model has shown that a natural substitutability condition characterizes the maximal domain of firm preferences for which the existence of stable allocations is guaranteed if the set of all existent contracts is acyclic. Moreover, it was argued that these conditions are sufficient to obtain a suitable lattice structure of 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 in order to recover an appropriate lattice structure.