{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T03:54:54Z","timestamp":1777607694127,"version":"3.51.4"},"reference-count":10,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2014,2,14]],"date-time":"2014-02-14T00:00:00Z","timestamp":1392336000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>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\u2019s 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.<\/jats:p>","DOI":"10.3390\/a7010032","type":"journal-article","created":{"date-parts":[[2014,2,14]],"date-time":"2014-02-14T12:37:22Z","timestamp":1392381442000},"page":"32-59","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Choice Function-Based Two-Sided Markets: Stability, Lattice Property, Path Independence and Algorithms"],"prefix":"10.3390","volume":"7","author":[{"given":"Tam\u00e0s","family":"Fleiner","sequence":"first","affiliation":[{"name":"Department of Computer Science and Information Theory, Budapest University of Technology and Economics, Magyar tud\u00f3sok k\u00f6r\u00fatja 2., Budapest 1117, Hungary"},{"name":"MTA-ELTE Egerv\u00e1ry Reseach Group, P\u00e1zm\u00e1ny P\u00e9ter s\u00e9t\u00e1ny 1\/C, Budapest 1117, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zsuzsanna","family":"Jank\u00f3","sequence":"additional","affiliation":[{"name":"Department of Operations Research, E\u00f6tv\u00f6s Lor\u00e1nd University, P\u00e1zm\u00e1ny P\u00e9ter s\u00e9t\u00e1ny 1\/C, Budapest 1117, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2014,2,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1080\/00029890.1962.11989827","article-title":"College admissions and the stability of marriage","volume":"69","author":"Gale","year":"1962","journal-title":"Am. Math. Mon."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1483","DOI":"10.2307\/1913392","article-title":"Job matching, coalition formation, and gross substitutes","volume":"50","author":"Kelso","year":"1982","journal-title":"Econometrica"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1287\/moor.13.4.619","article-title":"The lattice structure of the set of stable marriages with multiple partners","volume":"13","author":"Blair","year":"1988","journal-title":"Math. Oper. Res."},{"key":"ref_4","unstructured":"Ayg\u00fcn, O., and S\u00f6nmez, T. (2012). Matching with Contracts: The Critical Role of Irrelevance of Rejected Contracts, Mimeo, Boston College."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Azevedo, E.M., and Leshno, J.D. (2012). A Supply and Demand Framework for Two-Sided Matching Markets, The Second International Workshop on Matching Under Preferences. Working Paper; MATCH-UP 2012.","DOI":"10.2139\/ssrn.2260567"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"913","DOI":"10.1257\/0002828054825466","article-title":"Matching with contracts","volume":"95","author":"Hatfield","year":"2005","journal-title":"Am. Econ. Rev."},{"key":"ref_7","unstructured":"Knuth, D. (1976). Marriages Stables, Les Presses de l\u2019Universite de Montreal."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1287\/moor.28.1.103.14256","article-title":"A fixed-point approach to stable matchings and some applications","volume":"28","author":"Fleiner","year":"2003","journal-title":"Math. Oper. Res."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Bir\u00f3, P., and Kiselgof, S. (2013). College Admissions with Stable Score-Limits. Cent. Eur. J. Oper. Res., 1\u201315.","DOI":"10.1007\/s10100-013-0320-9"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"285","DOI":"10.2140\/pjm.1955.5.285","article-title":"A lattice-theoretical fixpoint theorem and its applications","volume":"5","author":"Tarski","year":"1955","journal-title":"Pac. J. Math."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/7\/1\/32\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:08:10Z","timestamp":1760216890000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/7\/1\/32"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,2,14]]},"references-count":10,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2014,3]]}},"alternative-id":["a7010032"],"URL":"https:\/\/doi.org\/10.3390\/a7010032","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,2,14]]}}}