Minimal Converse Consistent Extension of the Men Optimal Solution

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Minimal Converse Consistent Extension of the Men-Optimal Solution? I˙pek Ozkal-Sanver† November 8, 2009 Abstract In this paper we study two-sided, one-to-one matching problems and consider the most wellknown solution concept: the men-optimal solution. The men-optimal solution fails to satisfy consistency as well as converse consistency. Thanks to Sasaki and Toda (1992), we know that the minimal consistent extension of the men-optimal solution equals the core (Thomson, 1994a). In this paper, we compute the minimal converse consistent extension of the men-optimal solution as a correspondence which associates with each problem the set consist- ing of the men-optimal matching, and all stable and men-barterproof matchings for this problem. Key Words: Matching, Men-Optimal Solution, Consistency, Con- verse Consistency, JEL Classification Number: C78 ?I thank C¸ag˘atay Kayı for his helpful comments. Of course, all possible errors are mine. This work is part of the project 6= 107K560 supported by the Scientific and Technological Research Council of Turkey (TUBITAK). †Department of Economics, I˙stanbul Bilgi University, Turkey ; e-mail: isan- 1

consistency

serial men-dictatorship rules

matching µ

matching µ ?

let m1

men-barterproof matchings

minimal converse

w3 w2

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Publié par

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Thomson Consistency

Minimal Converse Consistent Extension of the ∗ Men-Optimal Solution

˙ ¨ † Ipek Ozkal-Sanver

November 8, 2009

Abstract In this paper we study two-sided, one-to-one matching problems and consider the most wellknown solution concept: the men-optimal solution. The men-optimal solution fails to satisfy consistency as well as converse consistency. Thanks to Sasaki and Toda (1992), we know that the minimal consistent extension of the men-optimal solution equals the core (Thomson, 1994athis paper, we compute the). In minimal converse consistent extension of the men-optimal solution as a correspondence which associates with each problem the set consist-ing of the men-optimal matching, and all stable and men-barterproof matchings for this problem. Key Words: Matching, Men-Optimal Solution, Consistency, Con-verse Consistency, JEL Classiﬁcation Number: C78

∗ Ithank¸Cag˘atayKayıforhishelpfulcomments.Ofcourse,allpossibleerrorsaremine. This work is part of the project6= 107K560 supported by the Scientiﬁc and Technological Research Council of Turkey (TUBITAK). ˙ † Department of Economics, Istanbul Bilgi University, Turkey ; e-mail: isan-ver@bilgi.edu.tr

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