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.
Similar content being viewed by others
References
G. Aşan M.R. Sanver (2003) Coalition structural games and the voluntary provision of public goods M.R. Sertel S. Koray (Eds) Advances in Economic Design Springer-Verlag Heidelberg 251–259
S Banerjee H. Konishi T. Sönmez (2001) ArticleTitleCore in a simple coalition formation game Social Choice and Welfare 18 135–153 Occurrence Handle10.1007/s003550000067
A. Bogomolnaia M.O. Jackson (2002) ArticleTitleThe stability of hedonic coalition structures Games and Economic Behavior 38 IssueID2 210–230 Occurrence Handle10.1006/game.2001.0877
S. Currarini M. Morelli (2001) ArticleTitleNetwork formation with sequential demands Review of Economic Design 5 229–249
J.H. Dreze J. Greenberg (1980) ArticleTitleHedonic coalitions: optimality and stability Econometrica 48 IssueID4 987–1003
Eren, N.I. (1993), Coalition Structural Games and Stability under Membership Property Rights Axioms, M.A. Thesis, Department of Economics, Boğaziçi University, İstanbul.
Greenberg J. (1977). Pure and local public goods: a game theoretic approach, Public Finance, in Sandmo, A. (ed), MA, Lexington, Heath and Co.
M.O. Jackson A. Wolinsky (1996) ArticleTitleA strategic model of social and economic networks Journal of Economic Theory 71 44–74 Occurrence Handle10.1006/jeth.1996.0108
D. Gale L. Shapley (1962) ArticleTitleCollege admissions and the stability of marriage American Mathematical Monthly 69 9–15
A.E. Roth M.A.O. Sotomayor (1990) Two-Sided Matching: A Study in Game-Theoretic Modelling and Analysis Cambridge University Press New York
H. Sasaki M. Toda (1992) ArticleTitleConsistency and characterization of the core of two-sided matching problems Journal of Economic Theory 56 218–237 Occurrence Handle10.1016/0022-0531(92)90078-V
M.R. Sertel (1982) Workers and Incentives North-Holland Amsterdam
M.R. Sertel (1992) Membership Property Rights, Efficiency and Stability Boğaziçi University Research Papers İstanbul
Sertel M.R. (1998), Designing Rights: Invisible Hand and Decentralizability Theorems, ASSET Lecture delivered at the annual meeting of ASSET in Bologna.
Sertel, M.R. (2003), Designing Rights, mimeo.
Author information
Authors and Affiliations
Corresponding author
Additional information
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
Rights and permissions
About this article
Cite this article
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
Issue Date:
DOI: https://doi.org/10.1007/s11238-005-0945-9