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Algorithms 2014, 7(1), 32-59; doi:10.3390/a7010032
Article

Choice Function-Based Two-Sided Markets: Stability, Lattice Property, Path Independence and Algorithms

1,2
 and 3,*
1 Department of Computer Science and Information Theory, Budapest University of Technology and Economics, Magyar tudósok körútja 2., Budapest 1117, Hungary 2 MTA-ELTE Egerváry Reseach Group, Pázmány Péter sétány 1/C, Budapest 1117, Hungary 3 Department of Operations Research, Eötvös Loránd University, Pázmány Péter sétány 1/C, Budapest 1117, Hungary
* Author to whom correspondence should be addressed.
Received: 23 June 2013 / Revised: 29 December 2013 / Accepted: 18 January 2014 / Published: 14 February 2014
(This article belongs to the Special Issue Special Issue on Matching under Preferences)
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Abstract

We build an abstract model, closely related to the stable marriage problem and motivated by Hungarian college admissions. We study different stability notions and show that an extension of the lattice property of stable marriages holds in these more general settings, even if the choice function on one side is not path independent. We lean on Tarski’s fixed point theorem and the substitutability property of choice functions. The main virtue of the work is that it exhibits practical, interesting examples, where non-path independent choice functions play a role, and proves various stability-related results.
Keywords: stable matchings; college admission; choice function; lattice stable matchings; college admission; choice function; lattice
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Fleiner, T.; Jankó, Z. Choice Function-Based Two-Sided Markets: Stability, Lattice Property, Path Independence and Algorithms. Algorithms 2014, 7, 32-59.

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