Abstract.
In order to treat a natural schedule matching problem related with worker-firm matchings, we generalize some theorems of Baiou–Balinski and Alkan–Gale by applying a fixed point method of Fleiner.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
H. Adachi, On a characterization of stable matchings, Econom. Lett., 68 (2000), 43–49.
A. Alkan and D. Gale, Stable schedule matching under revealed preference, J. Economic Theory, 112 (2003), 289–306.
M. Baiou and M. Balinski, The stable allocation (or ordinal transportation) problem, Math. Oper. Res., 27 (2002), 485–503.
C. Blair, The lattice structure of the set of stable matchings with multiple partners, Mathematics of Operations Research, 13 (1988), 619–628.
A. S. Kelso Jr. and V. P. Crawford, Job matching, coalition formation, and gross substitutes, Econometrica, 50 (1982), 1483–1504.
F. Echenique and J. Ovideo, Core many-to-one matchings by fixed-point methods, Journal of Economic Theory, 115 (2004), 358–376.
F. Echenique and J. Ovideo, A theory of stability in many-to-many matching markets, Theoretical Economics, 1 (2006), 233–273.
T. Feder, A new fixed point approach for stable networks and stable marriages, in: Twenty-First Symposium on the Theory of Computing (Seattle, WA, 1989), J. Comput. System Sci., 45 (1992), 233–284.
T. Fleiner, A matroid generalization of the stable matching polytope, in: Integer Programming and Combinatorial Optimization (Utrecht, 2001), Lecture Notes in Comput. Sci. 2081, Springer (Berlin, 2001), pp. 105–114.
T. Fleiner, Stable matchings through fixed points and graphs, Ann. Univ. Sci. Budapest. Eötvös, Sect. Math., 51 (2008), 69–116 (2009).
T. Fleiner, A fixed-point approach to stable matchings and some applications, Math. Oper. Res., 28 (2003), 103–126.
D. Gale and L. S. Shapley, College admissions and the stability of marriage, Amer. Math. Monthly, 69 (1962), 9–15.
J. W. Hatfield and P. Milgrom, Matching with contracts, American Economic Review, 95(4) (2005), 913–935.
B. Klaus and M. Walzl, Stable many-to-many matchings with contracts, Mathematics of Operations Research, 45 (2009), 422–434.
B. Knaster, Un théorème sur les fonctions d’ensembles, Ann. Soc. Polon. Math., 6 (1928), 133–134.
A. E. Roth, Stability and polarization of interests in job matching, Econometrica, 52(1) (1984), 47–57.
A. E. Roth and M. Sotomayor, Two-Sided Matching. A Study in Game-Theoretic Modeling and Analysis, Econometric Society Monographs 18, Cambridge University Press (Cambridge, 1990).
A. Subramanian, A new approach to stable matching problems, SIAM J. Comput., 23(4) (1994), 671–700.
A. Tarski, Quelques théorèmes généraux sur les images d’ensembles, Ann. Soc. Polon. Math., 6 (1928), 132–133.
A. Tarski, A lattice-theoretical fixpoint theorem and its applications, Pacific J. Math., 5 (1955), 285–310.
Author information
Authors and Affiliations
Corresponding author
Additional information
Corresponding author.
Rights and permissions
About this article
Cite this article
Komornik, V., Komornik, Z. & Viauroux, C.K. Stable schedule matchings. Acta Math Hung 135, 67–79 (2012). https://doi.org/10.1007/s10474-011-0165-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10474-011-0165-4