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A note on the lattice structure for matching markets via linear programming
Av. Italia 1556, San Luis, Argentina |
Given two stable matchings in a many-to-one matching market with $ q $-responsive preferences, by manipulating the objective function of the linear program that characterizes the stable matching set, we compute the least upper bound and greatest lower bound between them.
References:
[1] |
M. Baïou and M. Balinski,
The stable admissions polytope, Math. Program., 87 (2000), 427-439.
doi: 10.1007/s101070050004. |
[2] |
D. Gale and L. S. Shapley,
College admissions and the stability of marriage, Amer. Math. Monthly, 69 (1962), 9-15.
doi: 10.1080/00029890.1962.11989827. |
[3] |
A. E. Roth,
The college admissions problem is not equivalent to the marriage problem, J. Econom. Theory, 36 (1985), 277-288.
doi: 10.1016/0022-0531(85)90106-1. |
[4] |
A. E. Roth,
The evolution of the labor market for medical interns and residents: A case study in game theory, J. Political Econom., 92 (1984), 991-1016.
doi: 10.1086/261272. |
[5] |
A. E. Roth, U. G. Rothblum and and J. H. Vande Vate,
Stable matchings, optimal assignments, and linear programming, Math. Oper. Res., 18 (1993), 803-828.
doi: 10.1287/moor.18.4.803. |
[6] |
A. E. Roth and M. A. Sotomayor, Two-Sided Matching. A Study in Game-Theoretic Modeling and Analysis, Econometric Society Monographs, 18, Cambidge University Press, Cambridge, 1990.
doi: 10.1017/CCOL052139015X.![]() ![]() ![]() |
[7] |
U. G. Rothblum,
Characterization of stable matchings as extreme points of a polytope, Math. Programming, 54 (1992), 57-67.
doi: 10.1007/BF01586041. |
[8] |
A. Schrijver, Theory of Linear and Integer Programming, Wiley-Interscience Series in Discrete Mathematics, John Wiley & Sons, Ltd., Chichester, 1986. |
[9] |
J. Sethuraman, C.-P. Teo and L. Qian,
Many-to-one stable matching: Geometry and fairness, Math. Oper. Res., 31 (2006), 581-596.
doi: 10.1287/moor.1060.0207. |
[10] |
J. H. Vande Vate,
Linear programming brings marital bliss, Oper. Res. Lett., 8 (1989), 147-153.
doi: 10.1016/0167-6377(89)90041-2. |
show all references
References:
[1] |
M. Baïou and M. Balinski,
The stable admissions polytope, Math. Program., 87 (2000), 427-439.
doi: 10.1007/s101070050004. |
[2] |
D. Gale and L. S. Shapley,
College admissions and the stability of marriage, Amer. Math. Monthly, 69 (1962), 9-15.
doi: 10.1080/00029890.1962.11989827. |
[3] |
A. E. Roth,
The college admissions problem is not equivalent to the marriage problem, J. Econom. Theory, 36 (1985), 277-288.
doi: 10.1016/0022-0531(85)90106-1. |
[4] |
A. E. Roth,
The evolution of the labor market for medical interns and residents: A case study in game theory, J. Political Econom., 92 (1984), 991-1016.
doi: 10.1086/261272. |
[5] |
A. E. Roth, U. G. Rothblum and and J. H. Vande Vate,
Stable matchings, optimal assignments, and linear programming, Math. Oper. Res., 18 (1993), 803-828.
doi: 10.1287/moor.18.4.803. |
[6] |
A. E. Roth and M. A. Sotomayor, Two-Sided Matching. A Study in Game-Theoretic Modeling and Analysis, Econometric Society Monographs, 18, Cambidge University Press, Cambridge, 1990.
doi: 10.1017/CCOL052139015X.![]() ![]() ![]() |
[7] |
U. G. Rothblum,
Characterization of stable matchings as extreme points of a polytope, Math. Programming, 54 (1992), 57-67.
doi: 10.1007/BF01586041. |
[8] |
A. Schrijver, Theory of Linear and Integer Programming, Wiley-Interscience Series in Discrete Mathematics, John Wiley & Sons, Ltd., Chichester, 1986. |
[9] |
J. Sethuraman, C.-P. Teo and L. Qian,
Many-to-one stable matching: Geometry and fairness, Math. Oper. Res., 31 (2006), 581-596.
doi: 10.1287/moor.1060.0207. |
[10] |
J. H. Vande Vate,
Linear programming brings marital bliss, Oper. Res. Lett., 8 (1989), 147-153.
doi: 10.1016/0167-6377(89)90041-2. |
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