April  2015, 2(3&4): 201-206. doi: 10.3934/jdg.2015001

On Marilda Sotomayor's extraordinary contribution to matching theory

1. 

Instituto de Pesquisa Econômica Aplicada-IPEA, Avenida Presidente Antônio Carlos, 51, 20020-010, Rio de Janeiro, RJ, Brazil

2. 

Universitat Autònoma de Barcelona, Department of Economics and Economic History, Edifici B, 08193 Bellaterra, Spain

Received  April 2015 Revised  June 2015 Published  November 2015

We report on Marilda Sotomayor's extraordinay contribution to MatchingTheory on the occasion of her 70th anniversary.
Citation: Danilo Coelho, David Pérez-Castrillo. On Marilda Sotomayor's extraordinary contribution to matching theory. Journal of Dynamics and Games, 2015, 2 (3&4) : 201-206. doi: 10.3934/jdg.2015001
References:
[1]

F. Bardella and M. Stomayor, Redesenho e análise do mercado de admissão aos centros de pós-graduação em economia no Brasil à luz da teoria dos jogos: um experimento natural em desenho de mercados, Revista Brasileira de economia, 68 (2014), 425-455.

[2]

G. Demange, D. Gale and M. Sotomayor, Multi-item auctions, Journal of Political Economy, 94 (1986), 863-872.

[3]

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.

[4]

L. Dubins and D. Freedman, Machiavelli and the Gale-Shapley algorithm, American Mathematical Monthly, 88 (1981), 485-494. doi: 10.2307/2321753.

[5]

D. Gale and G. Demange, The strategy structure of two-sided matching markets, Econometrica, 53 (1985), 873-888. doi: 10.2307/1912658.

[6]

D. Gale and L. S. Shapley, College admissions and the stability of marriage, The American Mathematical Monthly, 69 (1962), 9-15. doi: 10.2307/2312726.

[7]

D. Gale and M. Sotomayor, Ms. Machiavelli and the stable matching problem, The American Mathematical Monthly, 92 (1985), 261-268. doi: 10.2307/2323645.

[8]

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.

[9]

A. S. Kelso and V. Crawford, Job matching, coalition formation and gross substitutes, Econometrica, 50 (1982), 1483-1504.

[10]

D. Knuth, Marriages Stables, Montreal: Les presses de l'université de Montreal. (English version in Knuth, D. (1991). Stable Marriages and Its Relation to Other Combinatorial Problems, CRM Proceedings and Lecture Notes, number 10, American Mathematical Society, Providence, Rhode Island), 1976.

[11]

D. Pérez-Castrillo and M. Sotomayor, A simple selling and buying procedure, Journal of Economic Theory, 103 (2002), 461-474. doi: 10.1006/jeth.2000.2783.

[12]

D. Pérez-Castrillo and M. Sotomayor, The manipulability and non-manipulability of competitive equilibrium rules in many-to-many buyer-seller markets, Working paper, 2014.

[13]

S. C. Rochford, Symmetrically pairwise-bargained allocations in an assignment market, Journal of Economic Theory, 34 (1984), 262-281. doi: 10.1016/0022-0531(84)90144-3.

[14]

A. 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.

[15]

A. Roth and M. Sotomayor, The college admissions problem revisited, Econometrica, 57 (1989), 559-570. doi: 10.2307/1911052.

[16]

A. Roth and M. Sotomayor, Two-sided Matching: A Study in Game-Theoretic Modeling and Analysis, Cambridge University Press and Econometric Society Monographs, 1990. doi: 10.1017/CCOL052139015X.

[17]

L. S. Shapley and M. Shubik, The assignment game I: The core, International Journal of Game Theory, 1 (1972), 111-130.

[18]

M. Sotomayor, On income fluctuations and capital gains, Journal of Economic Theory, 32 (1984), 14-35.

[19]

M. Sotomayor, The multiple partners game, In Equilibrium and Dynamics: Essays in Honor of David Gale, edit. Mukul Majumdar, Palgrave Macmillan, (1992), 322-354.

[20]

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.

[21]

M. Sotomayor, Mecanismo de admissão de candidatos às instituições. Modelagem e análise à luz da teoria dos jogos, Revista de Econometria, 16 (1996), 25-63.

[22]

M. Sotomayor, Three remarks on the stability of the many-to-many matching, Mathematical Social Sciences , 38 (1999), 55-70. doi: 10.1016/S0165-4896(98)00048-1.

[23]

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.

[24]

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.

[25]

M. Sotomayor, Reaching the core of the marriage market through a non-revelation mechanism, International Journal of Game Theory, 32 (2003), 241-251. doi: 10.1007/s001820300156.

[26]

M. Sotomayor, Some further remark on the core structure of the assignment game, Mathematical Social Sciences, 46 (2003), 261-265. doi: 10.1016/S0165-4896(03)00067-2.

[27]

M. Sotomayor, Implementation in the many to many matching market, Games and Economic Behavior, 46 (2004), 199-212. doi: 10.1016/S0899-8256(03)00047-2.

[28]

M. Sotomayor, Connecting the cooperative and competitive structures of the multiple-partners assignment game, Journal of Economic Theory, 134 (2007), 155-174. doi: 10.1016/j.jet.2006.02.005.

[29]

M. Sotomayor, Core structure and comparative statics in a hybrid matching market, Games and Economic Behavior, 60 (2007), 357-380. doi: 10.1016/j.geb.2006.12.001.

[30]

M. Sotomayor, The stability of the equilibrium outcomes in the admission games induced by stable matching rules, International Journal of Game Theory, (Special Issue in honor of David Gale) 36 (2008), 621-640. doi: 10.1007/s00182-008-0115-8.

[31]

M. Sotomayor, My encounters with David Gale, Games and Economic Behavior, 66 (2009), 643-646.

[32]

M. Sotomayor, Adjusting prices in the multiple-partners assignment game, International Journal of Game Theory, 38 (2009), 575-600. doi: 10.1007/s00182-009-0171-8.

[33]

M. Sotomayor, Encontros com David Gale, Mimeo, 2011. available at: https://www.fea.usp.br/feaecon/media/fck/File/ENCONTROS20COM20DAVID 20GALE(1).pdf.

[34]

M. Sotomayor, Modeling cooperative decision situations: The deviation function form and the equilibrium concept, Working paper, 2013.

show all references

References:
[1]

F. Bardella and M. Stomayor, Redesenho e análise do mercado de admissão aos centros de pós-graduação em economia no Brasil à luz da teoria dos jogos: um experimento natural em desenho de mercados, Revista Brasileira de economia, 68 (2014), 425-455.

[2]

G. Demange, D. Gale and M. Sotomayor, Multi-item auctions, Journal of Political Economy, 94 (1986), 863-872.

[3]

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.

[4]

L. Dubins and D. Freedman, Machiavelli and the Gale-Shapley algorithm, American Mathematical Monthly, 88 (1981), 485-494. doi: 10.2307/2321753.

[5]

D. Gale and G. Demange, The strategy structure of two-sided matching markets, Econometrica, 53 (1985), 873-888. doi: 10.2307/1912658.

[6]

D. Gale and L. S. Shapley, College admissions and the stability of marriage, The American Mathematical Monthly, 69 (1962), 9-15. doi: 10.2307/2312726.

[7]

D. Gale and M. Sotomayor, Ms. Machiavelli and the stable matching problem, The American Mathematical Monthly, 92 (1985), 261-268. doi: 10.2307/2323645.

[8]

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.

[9]

A. S. Kelso and V. Crawford, Job matching, coalition formation and gross substitutes, Econometrica, 50 (1982), 1483-1504.

[10]

D. Knuth, Marriages Stables, Montreal: Les presses de l'université de Montreal. (English version in Knuth, D. (1991). Stable Marriages and Its Relation to Other Combinatorial Problems, CRM Proceedings and Lecture Notes, number 10, American Mathematical Society, Providence, Rhode Island), 1976.

[11]

D. Pérez-Castrillo and M. Sotomayor, A simple selling and buying procedure, Journal of Economic Theory, 103 (2002), 461-474. doi: 10.1006/jeth.2000.2783.

[12]

D. Pérez-Castrillo and M. Sotomayor, The manipulability and non-manipulability of competitive equilibrium rules in many-to-many buyer-seller markets, Working paper, 2014.

[13]

S. C. Rochford, Symmetrically pairwise-bargained allocations in an assignment market, Journal of Economic Theory, 34 (1984), 262-281. doi: 10.1016/0022-0531(84)90144-3.

[14]

A. 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.

[15]

A. Roth and M. Sotomayor, The college admissions problem revisited, Econometrica, 57 (1989), 559-570. doi: 10.2307/1911052.

[16]

A. Roth and M. Sotomayor, Two-sided Matching: A Study in Game-Theoretic Modeling and Analysis, Cambridge University Press and Econometric Society Monographs, 1990. doi: 10.1017/CCOL052139015X.

[17]

L. S. Shapley and M. Shubik, The assignment game I: The core, International Journal of Game Theory, 1 (1972), 111-130.

[18]

M. Sotomayor, On income fluctuations and capital gains, Journal of Economic Theory, 32 (1984), 14-35.

[19]

M. Sotomayor, The multiple partners game, In Equilibrium and Dynamics: Essays in Honor of David Gale, edit. Mukul Majumdar, Palgrave Macmillan, (1992), 322-354.

[20]

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.

[21]

M. Sotomayor, Mecanismo de admissão de candidatos às instituições. Modelagem e análise à luz da teoria dos jogos, Revista de Econometria, 16 (1996), 25-63.

[22]

M. Sotomayor, Three remarks on the stability of the many-to-many matching, Mathematical Social Sciences , 38 (1999), 55-70. doi: 10.1016/S0165-4896(98)00048-1.

[23]

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.

[24]

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.

[25]

M. Sotomayor, Reaching the core of the marriage market through a non-revelation mechanism, International Journal of Game Theory, 32 (2003), 241-251. doi: 10.1007/s001820300156.

[26]

M. Sotomayor, Some further remark on the core structure of the assignment game, Mathematical Social Sciences, 46 (2003), 261-265. doi: 10.1016/S0165-4896(03)00067-2.

[27]

M. Sotomayor, Implementation in the many to many matching market, Games and Economic Behavior, 46 (2004), 199-212. doi: 10.1016/S0899-8256(03)00047-2.

[28]

M. Sotomayor, Connecting the cooperative and competitive structures of the multiple-partners assignment game, Journal of Economic Theory, 134 (2007), 155-174. doi: 10.1016/j.jet.2006.02.005.

[29]

M. Sotomayor, Core structure and comparative statics in a hybrid matching market, Games and Economic Behavior, 60 (2007), 357-380. doi: 10.1016/j.geb.2006.12.001.

[30]

M. Sotomayor, The stability of the equilibrium outcomes in the admission games induced by stable matching rules, International Journal of Game Theory, (Special Issue in honor of David Gale) 36 (2008), 621-640. doi: 10.1007/s00182-008-0115-8.

[31]

M. Sotomayor, My encounters with David Gale, Games and Economic Behavior, 66 (2009), 643-646.

[32]

M. Sotomayor, Adjusting prices in the multiple-partners assignment game, International Journal of Game Theory, 38 (2009), 575-600. doi: 10.1007/s00182-009-0171-8.

[33]

M. Sotomayor, Encontros com David Gale, Mimeo, 2011. available at: https://www.fea.usp.br/feaecon/media/fck/File/ENCONTROS20COM20DAVID 20GALE(1).pdf.

[34]

M. Sotomayor, Modeling cooperative decision situations: The deviation function form and the equilibrium concept, Working paper, 2013.

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