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Finding all stable matchings with couples
Why do stable clearinghouses work so well? - Small sets of stable matchings in typical environments, and the limits-on-manipulation theorem of Demange, Gale and Sotomayor
1. | Department of Economics, Stanford University, Landau Economics Building, 579 Serra Mall, Room 344, Stanford University, Stanford, CA 94305-6072, United States |
References:
[1] |
A. Abdulkadiroglu, P. A. Pathak and A. E. Roth, The New York City high school match, American Economic Review, Papers and Proceedings, 95 (2005), 364-367. |
[2] |
A. Abdulkadiroglu, P. A. Pathak and A. E. Roth, Strategy-proofness versus efficiency in matching with indifferences: Redesigning the NYC high school match, American Economic Review, 99 (2009), 1954-1978. |
[3] |
A. Abdulkadiroglu, P. A. Pathak, A. E. Roth and T. Sönmez, The Boston public school match, American Economic Review, Papers and Proceedings, 95 (2005), 368-371. |
[4] |
H. Adachi, On a characterization of stable matchings, Economics Letters, 68 (2000), 43-49.
doi: 10.1016/S0165-1765(99)00241-4. |
[5] |
I. Ashlagi, M. Braverman and A. Hassidim, Stability in large matching markets with complementarities, Operations Research, 62 (2014), 713-732.
doi: 10.1287/opre.2014.1276. |
[6] |
I. Ashlagi, Y. Kanoria and J. D. Leshno, Unbalanced random matching markets: The stark effect of competition,, Journal of Political Economy, ().
|
[7] |
A. Banerjee, E. Duflo, M. Ghatak and J. Lafortune, Marry for what: Caste and mate selection in modern India, American Economic Journal: Microeconomics, 5 (2013), 33-72. |
[8] |
G. S. Becker, A theory of marriage: Part I, Journal of Political Economy, 81 (1973), 813-846. |
[9] |
G. S. Becker, A theory of marriage: Part II, Journal of Political Economy, 82 (1974), S11-S26. |
[10] |
G. S. Becker, A Treatise on the Family, Harvard University Press, Cambridge MA, 1981. |
[11] |
P. A. Coles and R. I. Shorrer, Optimal truncation in matching markets, Games and Economic Behavior, 87 (2014), 591-615.
doi: 10.1016/j.geb.2014.01.005. |
[12] |
P. Coles, Y. Gonczarowski and R. I. Shorrer, Strategic behavior in unbalanced matching markets, Working Paper, 2014. Available from: http://scholar.harvard.edu/files/ran/files/cgs_0.pdf. |
[13] |
V. P. Crawford and E. M. Knoer, Job matching with heterogeneous firms and workers, Econometrica, 49 (1981), 437-450. |
[14] |
G. Demange and D. Gale, The strategy structure of 2-sided matching markets, Econometrica, 53 (1985), 873-888.
doi: 10.2307/1912658. |
[15] |
G. Demange, D. Gale and M. Sotomayor, Multi-item auctions, Journal of Political Economy, 94 (1986), 863-872. |
[16] |
G. Demange, D. Gale and M. Sotomayor, A further note on the stable matching problem, Discrete Applied Mathematics, 16 (1987), 217-222.
doi: 10.1016/0166-218X(87)90059-X. |
[17] |
L. E. Dubins and D. A. Freedman, Machiavelli and the gale-shapley algorithm, American Mathematical Monthly, 88 (1981), 485-494.
doi: 10.2307/2321753. |
[18] |
F. Echenique and J. Oviedo, Core many-to-one matchings by fixed-point methods, Journal of Economic Theory, 115 (2004), 358-376.
doi: 10.1016/S0022-0531(04)00042-1. |
[19] |
T. Fleiner, A fixed-point approach to stable matchings and some applications, Mathematics of Operations Research, 28 (2003), 103-126.
doi: 10.1287/moor.28.1.103.14256. |
[20] |
D. Gale and L. Shapley, College admissions and the stability of marriage, American Mathematical Monthly, 69 (1962), 9-15.
doi: 10.2307/2312726. |
[21] |
D. Gale and M. Sotomayor, Some remarks on the stable matching problem, Discrete Applied Mathematics, 11 (1985), 223-232.
doi: 10.1016/0166-218X(85)90074-5. |
[22] |
D. Gale and M. Sotomayor, Ms. machiavelli and the stable matching problem, American Mathematical Monthly, 92 (1985), 261-268.
doi: 10.2307/2323645. |
[23] |
J. Hatfield and P. Milgrom, Matching with contracts, American Economic Review 95 (2005), 913-935. |
[24] |
H. Günter, A. Hortaçsu and D. Ariely, Matching and sorting in online dating, American Economic Review, 100 (2010), 130-163. |
[25] |
R. Holzman and D. Samet, Matching of like rank and the size of the core in the marriage problem, Games and Economic Behavior 88 (2014), 277-285.
doi: 10.1016/j.geb.2014.10.003. |
[26] |
A. Hylland and R. Zeckhauser, The efficient allocation of individuals to positions, Journal of Political Economy, 87 (1979), 293-314. |
[27] |
N. Immorlica and M. Mahdian, Marriage, honesty, and stability, SODA 2005 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms, 2005, 53-62. |
[28] |
J. H. Kagel and A. E. Roth, The dynamics of reorganization in matching markets: A laboratory experiment motivated by a natural experiment, Quarterly Journal of Economics, 115 (2000), 201-235. |
[29] |
M. Kaneko and M. H. Wooders, Cores of partitioning games, Mathematical Social Sciences, 3 (1982), 313-327.
doi: 10.1016/0165-4896(82)90015-4. |
[30] |
A. S. Kelso, Jr. and V. P. Crawford, Job matching, coalition formation, and gross substitutes, Econometrica, 50 (1982), 1483-1504. |
[31] |
D. E. Knuth, Mariages Stables (French), Stable Mariages, Les Presses de l'Université de Montreal, Montreal, 1976. |
[32] |
D. E. Knuth, R. Motwani and B. Pittel, Stable husbands, Proceedings of the first annual ACM-SIAM Symposium on Discrete Algorithms, 1 (1990), 1-14.
doi: 10.1002/rsa.3240010102. |
[33] |
F. Kojima and P. A. Pathak, Incentives and stability in large two-sided matching markets, American Economic Review, 99 (2009), 608-627. |
[34] |
F. Kojima, P. A. Pathak and A. E. Roth, Matching with couples: Stability and incentives in large markets, Quarterly Journal of Economics, 128 (2013), 1585-1632. |
[35] |
T. C. Koopmans and M. Beckmann, Assignment problems and the location of economic activities, Econometrica, 25 (1957), 53-76.
doi: 10.2307/1907742. |
[36] |
D. G. McVitie, The stable marriage problem and the selection of students for university admission, M.Sc. Thesis, University of Newcastle upon Tyne, 1967. |
[37] |
D. G. McVitie and L. B. Wilson, Stable marriage assignments for unequal sets, BIT Numerical Mathematics, 10 (1970), 295-309. |
[38] |
D. G. McVitie and L. B. Wilson, The application of the stable marriage assignment to university admissions, Operational Research Quarterly, 21 (1970), 425-433. |
[39] |
D. G. McVitie and L. B. Wilson, The stable marriage problem, Communications of the ACM, 14 (1971), 486-490.
doi: 10.1145/362619.362631. |
[40] |
A. E. Roth, The economics of matching: Stability and incentives, Mathematics of Operations Research, 7 (1982), 617-628.
doi: 10.1287/moor.7.4.617. |
[41] |
A. E. Roth, Incentive compatibility in a market with indivisible goods, Economics Letters, 9 (1982), 127-132.
doi: 10.1016/0165-1765(82)90003-9. |
[42] |
A. E. Roth, The evolution of the labor market for medical interns and residents: A case study in game theory, Journal of Political Economy, 92 (1984), 991-1016. |
[43] |
A. E. Roth, Misrepresentation and stability in the marriage problem, Journal of Economic Theory, 34 (1984), 383-387.
doi: 10.1016/0022-0531(84)90152-2. |
[44] |
A. E. Roth, The college admissions problem is not equivalent to the marriage problem, Journal of Economic Theory, 36 (1985), 277-288.
doi: 10.1016/0022-0531(85)90106-1. |
[45] |
A. E. Roth, New physicians: A natural experiment in market organization, Science, 250 (1990), 1524-1528. |
[46] |
A. E. Roth, A natural experiment in the organization of entry level labor markets: Regional markets for new physicians and surgeons in the U.K., American Economic Review, 81 (1991), 415-440. |
[47] |
A. E. Roth and E. Peranson, The redesign of the matching market for american physicians: Some engineering aspects of economic design, American Economic Review, 89 (1999), 748-780. |
[48] |
A. E. Roth and M. Sotomayor, Interior points in the core of two-sided matching markets, Journal of Economic Theory, 45 (1988), 85-101.
doi: 10.1016/0022-0531(88)90255-4. |
[49] |
A. E. Roth and M.a Sotomayor, The college admissions problem revisited, Econometrica, 57 (1989), 559-570.
doi: 10.2307/1911052. |
[50] |
A. E. Roth and M. Sotomayor, Two-sided Matching: A Study in Game-Theoretic Modeling and Analysis, Cambridge University Press, 1990.
doi: 10.1017/CCOL052139015X. |
[51] |
L. S. Shapley and M. Shubik, The assignment game I: The core, International Journal of Game Theory, 1 (1972), 111-130. |
[52] |
M. Sotomayor, A non-constructive elementary proof of the existence of stable marriages, Games and Economic Behavior, 13 (1996), 135-137.
doi: 10.1006/game.1996.0029. |
[53] |
M. Sotomayor, The lattice structure of the set of stable outcomes of the multiple partners assignment game, International Journal of Game Theory, 28 (1999), 567-583.
doi: 10.1007/s001820050126. |
[54] |
M. Sotomayor, Existence of stable outcomes and the lattice property for a unified matching market, Mathematical Social Sciences, 39 (2000), 119-132.
doi: 10.1016/S0165-4896(99)00028-1. |
[55] |
M. Sotomayor, An elementary non-constructive proof of the non-emptiness of the core of the housing market of Shapley and Scarf, Mathematical Social Sciences, 50 (2005), 298-303.
doi: 10.1016/j.mathsocsci.2005.04.004. |
show all references
References:
[1] |
A. Abdulkadiroglu, P. A. Pathak and A. E. Roth, The New York City high school match, American Economic Review, Papers and Proceedings, 95 (2005), 364-367. |
[2] |
A. Abdulkadiroglu, P. A. Pathak and A. E. Roth, Strategy-proofness versus efficiency in matching with indifferences: Redesigning the NYC high school match, American Economic Review, 99 (2009), 1954-1978. |
[3] |
A. Abdulkadiroglu, P. A. Pathak, A. E. Roth and T. Sönmez, The Boston public school match, American Economic Review, Papers and Proceedings, 95 (2005), 368-371. |
[4] |
H. Adachi, On a characterization of stable matchings, Economics Letters, 68 (2000), 43-49.
doi: 10.1016/S0165-1765(99)00241-4. |
[5] |
I. Ashlagi, M. Braverman and A. Hassidim, Stability in large matching markets with complementarities, Operations Research, 62 (2014), 713-732.
doi: 10.1287/opre.2014.1276. |
[6] |
I. Ashlagi, Y. Kanoria and J. D. Leshno, Unbalanced random matching markets: The stark effect of competition,, Journal of Political Economy, ().
|
[7] |
A. Banerjee, E. Duflo, M. Ghatak and J. Lafortune, Marry for what: Caste and mate selection in modern India, American Economic Journal: Microeconomics, 5 (2013), 33-72. |
[8] |
G. S. Becker, A theory of marriage: Part I, Journal of Political Economy, 81 (1973), 813-846. |
[9] |
G. S. Becker, A theory of marriage: Part II, Journal of Political Economy, 82 (1974), S11-S26. |
[10] |
G. S. Becker, A Treatise on the Family, Harvard University Press, Cambridge MA, 1981. |
[11] |
P. A. Coles and R. I. Shorrer, Optimal truncation in matching markets, Games and Economic Behavior, 87 (2014), 591-615.
doi: 10.1016/j.geb.2014.01.005. |
[12] |
P. Coles, Y. Gonczarowski and R. I. Shorrer, Strategic behavior in unbalanced matching markets, Working Paper, 2014. Available from: http://scholar.harvard.edu/files/ran/files/cgs_0.pdf. |
[13] |
V. P. Crawford and E. M. Knoer, Job matching with heterogeneous firms and workers, Econometrica, 49 (1981), 437-450. |
[14] |
G. Demange and D. Gale, The strategy structure of 2-sided matching markets, Econometrica, 53 (1985), 873-888.
doi: 10.2307/1912658. |
[15] |
G. Demange, D. Gale and M. Sotomayor, Multi-item auctions, Journal of Political Economy, 94 (1986), 863-872. |
[16] |
G. Demange, D. Gale and M. Sotomayor, A further note on the stable matching problem, Discrete Applied Mathematics, 16 (1987), 217-222.
doi: 10.1016/0166-218X(87)90059-X. |
[17] |
L. E. Dubins and D. A. Freedman, Machiavelli and the gale-shapley algorithm, American Mathematical Monthly, 88 (1981), 485-494.
doi: 10.2307/2321753. |
[18] |
F. Echenique and J. Oviedo, Core many-to-one matchings by fixed-point methods, Journal of Economic Theory, 115 (2004), 358-376.
doi: 10.1016/S0022-0531(04)00042-1. |
[19] |
T. Fleiner, A fixed-point approach to stable matchings and some applications, Mathematics of Operations Research, 28 (2003), 103-126.
doi: 10.1287/moor.28.1.103.14256. |
[20] |
D. Gale and L. Shapley, College admissions and the stability of marriage, American Mathematical Monthly, 69 (1962), 9-15.
doi: 10.2307/2312726. |
[21] |
D. Gale and M. Sotomayor, Some remarks on the stable matching problem, Discrete Applied Mathematics, 11 (1985), 223-232.
doi: 10.1016/0166-218X(85)90074-5. |
[22] |
D. Gale and M. Sotomayor, Ms. machiavelli and the stable matching problem, American Mathematical Monthly, 92 (1985), 261-268.
doi: 10.2307/2323645. |
[23] |
J. Hatfield and P. Milgrom, Matching with contracts, American Economic Review 95 (2005), 913-935. |
[24] |
H. Günter, A. Hortaçsu and D. Ariely, Matching and sorting in online dating, American Economic Review, 100 (2010), 130-163. |
[25] |
R. Holzman and D. Samet, Matching of like rank and the size of the core in the marriage problem, Games and Economic Behavior 88 (2014), 277-285.
doi: 10.1016/j.geb.2014.10.003. |
[26] |
A. Hylland and R. Zeckhauser, The efficient allocation of individuals to positions, Journal of Political Economy, 87 (1979), 293-314. |
[27] |
N. Immorlica and M. Mahdian, Marriage, honesty, and stability, SODA 2005 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms, 2005, 53-62. |
[28] |
J. H. Kagel and A. E. Roth, The dynamics of reorganization in matching markets: A laboratory experiment motivated by a natural experiment, Quarterly Journal of Economics, 115 (2000), 201-235. |
[29] |
M. Kaneko and M. H. Wooders, Cores of partitioning games, Mathematical Social Sciences, 3 (1982), 313-327.
doi: 10.1016/0165-4896(82)90015-4. |
[30] |
A. S. Kelso, Jr. and V. P. Crawford, Job matching, coalition formation, and gross substitutes, Econometrica, 50 (1982), 1483-1504. |
[31] |
D. E. Knuth, Mariages Stables (French), Stable Mariages, Les Presses de l'Université de Montreal, Montreal, 1976. |
[32] |
D. E. Knuth, R. Motwani and B. Pittel, Stable husbands, Proceedings of the first annual ACM-SIAM Symposium on Discrete Algorithms, 1 (1990), 1-14.
doi: 10.1002/rsa.3240010102. |
[33] |
F. Kojima and P. A. Pathak, Incentives and stability in large two-sided matching markets, American Economic Review, 99 (2009), 608-627. |
[34] |
F. Kojima, P. A. Pathak and A. E. Roth, Matching with couples: Stability and incentives in large markets, Quarterly Journal of Economics, 128 (2013), 1585-1632. |
[35] |
T. C. Koopmans and M. Beckmann, Assignment problems and the location of economic activities, Econometrica, 25 (1957), 53-76.
doi: 10.2307/1907742. |
[36] |
D. G. McVitie, The stable marriage problem and the selection of students for university admission, M.Sc. Thesis, University of Newcastle upon Tyne, 1967. |
[37] |
D. G. McVitie and L. B. Wilson, Stable marriage assignments for unequal sets, BIT Numerical Mathematics, 10 (1970), 295-309. |
[38] |
D. G. McVitie and L. B. Wilson, The application of the stable marriage assignment to university admissions, Operational Research Quarterly, 21 (1970), 425-433. |
[39] |
D. G. McVitie and L. B. Wilson, The stable marriage problem, Communications of the ACM, 14 (1971), 486-490.
doi: 10.1145/362619.362631. |
[40] |
A. E. Roth, The economics of matching: Stability and incentives, Mathematics of Operations Research, 7 (1982), 617-628.
doi: 10.1287/moor.7.4.617. |
[41] |
A. E. Roth, Incentive compatibility in a market with indivisible goods, Economics Letters, 9 (1982), 127-132.
doi: 10.1016/0165-1765(82)90003-9. |
[42] |
A. E. Roth, The evolution of the labor market for medical interns and residents: A case study in game theory, Journal of Political Economy, 92 (1984), 991-1016. |
[43] |
A. E. Roth, Misrepresentation and stability in the marriage problem, Journal of Economic Theory, 34 (1984), 383-387.
doi: 10.1016/0022-0531(84)90152-2. |
[44] |
A. E. Roth, The college admissions problem is not equivalent to the marriage problem, Journal of Economic Theory, 36 (1985), 277-288.
doi: 10.1016/0022-0531(85)90106-1. |
[45] |
A. E. Roth, New physicians: A natural experiment in market organization, Science, 250 (1990), 1524-1528. |
[46] |
A. E. Roth, A natural experiment in the organization of entry level labor markets: Regional markets for new physicians and surgeons in the U.K., American Economic Review, 81 (1991), 415-440. |
[47] |
A. E. Roth and E. Peranson, The redesign of the matching market for american physicians: Some engineering aspects of economic design, American Economic Review, 89 (1999), 748-780. |
[48] |
A. E. Roth and M. Sotomayor, Interior points in the core of two-sided matching markets, Journal of Economic Theory, 45 (1988), 85-101.
doi: 10.1016/0022-0531(88)90255-4. |
[49] |
A. E. Roth and M.a Sotomayor, The college admissions problem revisited, Econometrica, 57 (1989), 559-570.
doi: 10.2307/1911052. |
[50] |
A. E. Roth and M. Sotomayor, Two-sided Matching: A Study in Game-Theoretic Modeling and Analysis, Cambridge University Press, 1990.
doi: 10.1017/CCOL052139015X. |
[51] |
L. S. Shapley and M. Shubik, The assignment game I: The core, International Journal of Game Theory, 1 (1972), 111-130. |
[52] |
M. Sotomayor, A non-constructive elementary proof of the existence of stable marriages, Games and Economic Behavior, 13 (1996), 135-137.
doi: 10.1006/game.1996.0029. |
[53] |
M. Sotomayor, The lattice structure of the set of stable outcomes of the multiple partners assignment game, International Journal of Game Theory, 28 (1999), 567-583.
doi: 10.1007/s001820050126. |
[54] |
M. Sotomayor, Existence of stable outcomes and the lattice property for a unified matching market, Mathematical Social Sciences, 39 (2000), 119-132.
doi: 10.1016/S0165-4896(99)00028-1. |
[55] |
M. Sotomayor, An elementary non-constructive proof of the non-emptiness of the core of the housing market of Shapley and Scarf, Mathematical Social Sciences, 50 (2005), 298-303.
doi: 10.1016/j.mathsocsci.2005.04.004. |
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