Abstract
We define two versions of stability and efficiency of partitions and analyze their relationships for some matching rules. The stability and efficiency of a partition depends on the matching rule φ. The results are stated under various membership property rights axioms. It is shown that in a world where agents can freely exit from and enter coalitions, whenever the matching rule is individually rational and Pareto optimal, the set of φ-stable and φ-efficient partitions coincide and it is unique: the grand coalition. Then we define a weaker version of stability and efficiency, namely specific to a given preference profile and find some negative results for stable matching rules.
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I dedicate this manuscript to the memory of my dear teacher and colleague Murat R. Sertel. I thank Semih Koray, İsmail Sağlam, Remzi Sanver, Tayfun Sönmez, William Thomson, Sylvie Thoron and an anonymous referee for their helpful comments. All remaining errors are my own responsibility. JEL Classification: C78
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Özkal-Sanver, İ. Stability and Efficiency of Partitions in Matching Problems. Theor Decis 59, 193–205 (2005). https://doi.org/10.1007/s11238-005-0945-9
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DOI: https://doi.org/10.1007/s11238-005-0945-9