This paper is focused on the analysis, in the framework
of lattice theory, of the matchings obtained from restabilization (after disruption) of stable matchings. When the disruption is due to entry workers or
closure of firms the unemployed workers make offers to firms. The stable
matching obtained is the firms-worst stable matching of the set of stable matchings
that the firms weakly prefer to the initial stable matching (i.e., before being disrupted by changes
in the population). More precisely, their position within the lattice of stable
matchings is shown.
References
[1]
Blair, C. (1988) The Lattice Structure of the Set of Stable Matchings with Multiple Partners. Mathematics of Operations Research, 13, 619-628. https://doi.org/10.1287/moor.13.4.619
[2]
Blum, Y., Roth, A.E. and Rothblum, U.G. (1997) Vacancy Chains and Equilibration in Senior-Level Labor Markets. Journal of Economic Theory, 76, 362-411. https://doi.org/10.1006/jeth.1997.2307
[3]
Gale, D. and Shapley, L. (1962) Collage Admissions and Stability of Marriage. The American Mathematical Monthly, 69, 9-15. https://doi.org/10.1080/00029890.1962.11989827
[4]
Cantala, D. (2004) Restabilizing Matching Markets at Senior Level. Games and Economic Behavior, 48, 1-17. https://doi.org/10.1016/j.geb.2003.07.005
[5]
Cantala, D. (2011) Agreement toward Stability in Matching Markets. Review of Economic Design, 15, 293-316. https://doi.org/10.1007/s10058-009-0098-3
[6]
Wu, Q.Y. and Roth, A.E. (2018) The Lattice of Envy-Free Matchings. Games and Economic Behavior, 109, 201-211. https://doi.org/10.1016/j.geb.2017.12.016
[7]
Sotomayor M. (1996) A Non-Constructive Elementary Proof of the Existence of Stable Marriages. Games and Economic Behavior, 13, 135-137. https://doi.org/10.1006/game.1996.0029
[8]
Martnez R. and Massó J. and Neme A. and Oviedo J. (2000) Single Agents and the Set of Many-to-One Stable Matchings. Journal of Economic Theory, 91, 91-105. https://doi.org/10.1006/jeth.1999.2586
[9]
Kelso, A.S. and Crawford, V.P. (1982) Job Matching, Coalition Formation, and Gross Substitutes. Econometrica, 50, 1483-1504. https://doi.org/10.2307/1913392
[10]
Roth, A. (1984) Stability and Polarization of Interests in Job Matching. Econometrica, 52, 47-57. https://doi.org/10.2307/1911460
[11]
Martnez, R. and Massó, J. and Neme, A. and Oviedo, J. (2001) On the Lattice Structure of the Set of Stable Matchings for a Many-to-One Model. Optimization, 50, 439-457. https://doi.org/10.1080/02331930108844574
