On preferences over subsets and the lattice structure of stable matchings

被引：11

作者：

Alkan A. ^{[1
]}

机构：

[1] Sabanci University

来源：

Review of Economic Design | 2001年 / 6卷 / 1期

关键词：

Choice function; Lattice; Revealed preference; Stable matchings;

D O I：

10.1007/PL00013699

中图分类号：

学科分类号：

摘要：

This paper studies the structure of stable multipartner matchings in two-sided markets where choice functions are quotafilling in the sense that they satisfy the substitutability axiom and, in addition, fill a quota whenever possible. It is shown that (i) the set of stable matchings is a lattice under the common revealed preference orderings of all agents on the same side, (ii) the supremum (infimum) operation of the lattice for each side consists componentwise of the join (meet) operation in the revealed preference ordering of the agents on that side, and (iii) the lattice has the polarity, distributivity, complementariness and full-quota properties. © Springer-Verlag 2001.

引用

页码：99 / 111

页数：12

共 13 条

[1]

Aizerman M., Aleskerov F., Theory of Choice, (1995)

[2]

Aizerman M., Malishevski A.V., General theory of best variants choice, IEEE Trans. Automatic Ontrol AC, 26, 5, pp. 1030-1041, (1979)

[3]

Alkan A., On the properties of stable many-to-many matchings under responsive preferences, Current Trends in Economics: Theory and Applications Studies in Economic Theory, 8, (1999)

[4]

Baiou M., Balinski M., Many-to-many Matching: Stable Polyandrous Polygamy (Or Polygamous Polyandry), (1998)

[5]

Birkhoff G., Lattice Theory, 25, (1973)

[6]

Blair C., The lattice structure of the set of stable matchings with multiple partners, Mathematics of Operations Research, 13, pp. 619-628, (1988)

[7]

Gusfield D., Irving R.W., The Stable Marriage Problem: Structure and Algorithms, (1989)

[8]

Koshevoy G.A., Choice functions and abstract convex geometries, Mathematical Social Sciences, 38, 1, pp. 35-44, (1999)

[9]

Monjardet B.V., Raderanirina V., The duality between the anti-exchange closure operators and the path independent choice operators on a finite set. mimeo, CERMSEM, (1999)

[10]

Martinez R., Masso J., Neme A., Oviedo J., Single Agents and the Set of Many-to-one Stable Matchings, (1999)

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