zbMATH — the first resource for mathematics

Stability in dynamic matching markets. (English) Zbl 1099.91076
Summary: A dynamic two-sided matching market is considered. We examine two existing notions of stability-the core and recursive core-for this multi-period market and argue that they both have limitations. We define two new notions of stability and label them, self-sustaining stability and strict self-sustaining stability. Both concepts can be viewed as the recursive core with more stringent conditions for when deviating coalitions are effective. We show that these concepts overcome some of the weaknesses of the core and the recursive core. We also provide conditions for the existence of our concepts.

91B68 Matching models
91B62 Economic growth models
Full Text: DOI
[1] Bhattacharya, A., Coalitional stability with a credibility constraint, Math. soc. sci., 43, 27-44, (2002) · Zbl 1021.91003
[2] Becker, R.A.; Chakrabarti, S.K., The recursive core, Econometrica, 63, 401-423, (1995) · Zbl 0835.90014
[3] Bernheim, B.D.; Peleg, B.; Whinston, M.D., Coalition-proof Nash equilibria; I: concepts, J. econ. theory, 42, 1-12, (1987) · Zbl 0619.90090
[4] Blum, Y.; Roth, A.E.; Rothblum, U.G., Vacancy chains and equilibration in senior-level labor markets, J. econ. theory, 76, 362-411, (1997) · Zbl 0892.90047
[5] Chwe, M.S.Y., Farsighted coalitional stability, J. econ. theory, 63, 299-325, (1994) · Zbl 0841.90131
[6] Damiano, E., Lam, R., 2001. Self-sustaining stability in dynamic marriage markets. Mimeo. University of Toronto
[7] Gale, D., Money in equilibrium, (1982), Cambridge Univ. Press Cambridge · Zbl 0531.90011
[8] Gale, D.; Shapley, D., College admissions and the stability of marriage, Amer. math. monthly, 69, 9-15, (1962) · Zbl 0109.24403
[9] Klijn, F.; Mass√≥, J., Weak stability and a bargaining set for the marriage model, Games econ. behav., 42, 91-100, (2003) · Zbl 1032.91095
[10] Konishi, H.; Ray, D., Coalition formation as a dynamic process, J. econ. theory, 110, 1-41, (2003) · Zbl 1052.91017
[11] Ray, D., Credible coalitions and the core, Int. J. game theory, 18, 185-187, (1989) · Zbl 0719.90099
[12] Roth, A.E.; Sotomayor, M.A.O., Two-sided matching: A study in game-theoretic modeling and analysis, (1990), Cambridge Univ. Press Cambridge · Zbl 0726.90003
[13] Roth, A.E.; Vande Vate, J.H., Random paths to stability in two-sided matching, Econometrica, 58, 1475-1480, (1990) · Zbl 0731.90007
[14] Rubinstein, A., Strong perfect equilibrium in supergames, Int. J. game theory, 9, 1-12, (1990) · Zbl 0433.90093
[15] Zhou, L., A new bargaining set of an N-person game and endogenous coalition formation, Games econ. behav., 6, 512-526, (1994) · Zbl 0807.90143
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.