March & 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 & 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.   Google Scholar

[2]

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

[3]

G. Demange, D. Gale and M. Sotomayor, A further note on the stable matching problem,, Discrete Applied Mathematics, 16 (1987), 217.  doi: 10.1016/0166-218X(87)90059-X.  Google Scholar

[4]

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

[5]

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

[6]

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

[7]

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

[8]

D. Gale and M. Sotomayor, Some remarks on the stable matching problem,, Discrete Applied Mathematics, 11 (1985), 223.  doi: 10.1016/0166-218X(85)90074-5.  Google Scholar

[9]

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

[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, (1976).   Google Scholar

[11]

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

[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).   Google Scholar

[13]

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

[14]

A. Roth and M. Sotomayor, Interior points in the core of two-sided matching markets,, Journal of Economic Theory, 45 (1988), 85.  doi: 10.1016/0022-0531(88)90255-4.  Google Scholar

[15]

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

[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.  Google Scholar

[17]

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

[18]

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

[19]

M. Sotomayor, The multiple partners game,, In Equilibrium and Dynamics: Essays in Honor of David Gale, (1992), 322.   Google Scholar

[20]

M. Sotomayor, A non-constructive elementary proof of the existence of stable marriages,, Games and Economic Behavior, 13 (1996), 135.  doi: 10.1006/game.1996.0029.  Google Scholar

[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.   Google Scholar

[22]

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

[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.  doi: 10.1007/s001820050126.  Google Scholar

[24]

M. Sotomayor, Existence of stable outcomes and the lattice property for a unified matching market,, Mathematical Social Sciences, 39 (2000), 119.  doi: 10.1016/S0165-4896(99)00028-1.  Google Scholar

[25]

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

[26]

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

[27]

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

[28]

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

[29]

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

[30]

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

[31]

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

[32]

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

[33]

M. Sotomayor, Encontros com David Gale,, Mimeo, (2011).   Google Scholar

[34]

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

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.   Google Scholar

[2]

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

[3]

G. Demange, D. Gale and M. Sotomayor, A further note on the stable matching problem,, Discrete Applied Mathematics, 16 (1987), 217.  doi: 10.1016/0166-218X(87)90059-X.  Google Scholar

[4]

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

[5]

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

[6]

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

[7]

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

[8]

D. Gale and M. Sotomayor, Some remarks on the stable matching problem,, Discrete Applied Mathematics, 11 (1985), 223.  doi: 10.1016/0166-218X(85)90074-5.  Google Scholar

[9]

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

[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, (1976).   Google Scholar

[11]

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

[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).   Google Scholar

[13]

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

[14]

A. Roth and M. Sotomayor, Interior points in the core of two-sided matching markets,, Journal of Economic Theory, 45 (1988), 85.  doi: 10.1016/0022-0531(88)90255-4.  Google Scholar

[15]

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

[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.  Google Scholar

[17]

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

[18]

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

[19]

M. Sotomayor, The multiple partners game,, In Equilibrium and Dynamics: Essays in Honor of David Gale, (1992), 322.   Google Scholar

[20]

M. Sotomayor, A non-constructive elementary proof of the existence of stable marriages,, Games and Economic Behavior, 13 (1996), 135.  doi: 10.1006/game.1996.0029.  Google Scholar

[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.   Google Scholar

[22]

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

[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.  doi: 10.1007/s001820050126.  Google Scholar

[24]

M. Sotomayor, Existence of stable outcomes and the lattice property for a unified matching market,, Mathematical Social Sciences, 39 (2000), 119.  doi: 10.1016/S0165-4896(99)00028-1.  Google Scholar

[25]

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

[26]

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

[27]

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

[28]

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

[29]

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

[30]

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

[31]

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

[32]

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

[33]

M. Sotomayor, Encontros com David Gale,, Mimeo, (2011).   Google Scholar

[34]

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

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