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A survey on assignment markets
1. | Departament de Matemàtica Econòmica, Financera i Actuarial, Universitat de Barcelona, Av. Diagonal, 690, 08034 Barcelona, Spain, Spain |
References:
[1] |
R. P. Arribillaga, J. Massó and A. Neme, On the structure of cooperative and competitive solutions of a generalized assignment game, Journal of Applied Mathematics, (2014), Art. ID 190614, 20 pp.
doi: 10.1155/2014/190614. |
[2] |
L. M. Ausubel and P. Milgrom, Ascending auctions with package bidding, Frontiers of Theoretical Economics, 1 (2002), 44pp(Republished in BePress Advances in Theoretical Economics).
doi: 10.2202/1534-5955.1019. |
[3] |
L. M. Ausubel and P. Milgrom, The lovely but lonely Vickrey auction, In Combinatorial Auctions (ed. P. Cramton, R. Steinberg and Y. Shoham), MIT Press, 2005. |
[4] |
L. M. Ausubel and P. Milgrom, Ascending Proxy Auctions, In Combinatorial Auctions (ed. P. Cramton, R. Steinberg and Y. Shoham), MIT Press, 2005. |
[5] |
M. L. Balinski and D. Gale, On the core of the assignment game, In Functional Analysis, Optimization and Mathematical Economics (ed. L.J. Leifman), Oxford University (1990), 274-289. |
[6] |
S. Bikhchandani and J. M. Ostroy, The package assignment model, Journal of Economic Theory, 107 (2002), 377-406.
doi: 10.1006/jeth.2001.2957. |
[7] |
G. Birkhoff, Tres observaciones sobre el álgebra lineal, Revista Universidad Nacional de Tucuman, Series A, 5 (1946), 147-151. |
[8] |
R. van den Brink and M. Pintér, On axiomatizations of the Shapley value for assignment games, Journal of Mathematical Economics, 60 (2015), 110-114.
doi: 10.1016/j.jmateco.2015.06.016. |
[9] |
E. Camiña, A generalized assignment game, Mathematical Social Sciences, 52 (2006), 152-161.
doi: 10.1016/j.mathsocsci.2006.06.003. |
[10] |
V. P. Crawford and E. M. Knoer, Job matching with heterogeneous firms and workers, Econometrica, 49 (1981), 437-450.
doi: 10.2307/1913320. |
[11] |
M. Davis and M. Maschler, The kernel of a cooperative game, Naval Research Logistics Quarterly 12 (1965), 223-259.
doi: 10.1002/nav.3800120303. |
[12] |
G. Demange, Strategyproofness in the Assignment Market Game, Laboratoire d'Econometrie de l'Ecole Polytechnique, Paris, Mimeo, 1982. |
[13] |
G. Demange and D. Gale, The strategy structure of two-sided matching markets, Econometrica, 53 (1985), 873-888.
doi: 10.2307/1912658. |
[14] |
G. Demange, D. Gale and M. Sotomayor, Multi-item auctions, Journal of Political Economy, 94 (1986), 863-872.
doi: 10.1086/261411. |
[15] |
T. S. H. Driessen, A note on the inclusion of the kernel in the core of the bilateral assignment game, International Journal of Game Theory, 27 (1998), 301-303.
doi: 10.1007/s001820050073. |
[16] |
A. Fagebaume, D. Gale and M. Sotomayor, A note on the multiple-partners assignment game, Journal of Mathematical Economics, 46 (2010), 388-392.
doi: 10.1016/j.jmateco.2009.06.014. |
[17] |
D. Gale, The Theory of Linear Economic Models, McGraw-Hill, New York, 1960. |
[18] |
D. Gale and L. S. Shapley, College Admission and the Stability of Marriage, American Mathematical Monthly, 69 (1962), 9-15.
doi: 10.2307/2312726. |
[19] |
H. Hamers, F. Klijn, T. Solymosi, S. Tijs and J. P. Villar, Assignment games satisfy the CoMa-property, Games and Economic Behavior, 38 (2002), 231-239. |
[20] |
M. Hoffmann and P. Sudhölter, The Shapley value of exact assignment games, International Journal of Game Theory 35 (2007), 557-568.
doi: 10.1007/s00182-006-0068-8. |
[21] |
J. M. Izquierdo, M. Núñez and C. Rafels, A simple procedure to obtain the extreme core allocations of an assignment market, International Journal of Game Theory, 36 (2007), 17-26.
doi: 10.1007/s00182-007-0091-4. |
[22] |
D. Jaume, J. Massó and A. Neme, The multiple-partners assignment game with heterogeneous sales and multi-unit demands: competitive equilibria, Mathematical Methods of Operations Research, 76 (2012), 161-187.
doi: 10.1007/s00186-012-0395-4. |
[23] |
M. Kaneko, On the core and competitive equilibria of a market with indivisible goods, Naval Research Logistics Quarterly, 23 (1976), 321-337.
doi: 10.1002/nav.3800230214. |
[24] |
M. Kaneko, The central assignment game and the assignment markets, Journal of Mathematical Economics, 10 (1982), 205-232.
doi: 10.1016/0304-4068(82)90038-6. |
[25] |
M. Kaneko and M. Wooders, Cores of partitioning games, Mathematical Social Sciences, 3 (1982), 313-327.
doi: 10.1016/0165-4896(82)90015-4. |
[26] |
T. C. Koopmans and M. Beckmann, Assignment Problems and the Location of Economic Activities, Econometrica, 25 (1957), 53-76.
doi: 10.2307/1907742. |
[27] |
H. B. Leonard, Elicitation of honest preferences for the assignment of individuals to positions, Journal of Political Economy, 91 (1983), 461-479.
doi: 10.1086/261158. |
[28] |
F. Llerena and M. Núñez, A geometric characterization of the nucleolus of the assignment game, Economics Bulletin 31 (2011), 3275-3285. |
[29] |
F. Llerena, M. Núñez and C. Rafels, An axiomatization of the nucleolus of the assignment game, International Journal of Game Theory, 44 (2015), 1-15.
doi: 10.1007/s00182-014-0416-z. |
[30] |
W. F. Lucas, A game with no solution, Bulletin of the American Mathematical Society, 74 (1968), 237-239.
doi: 10.1090/S0002-9904-1968-11901-9. |
[31] |
W. F. Lucas, Core theory for multiple-sided assignment games, Duke Mathematical Journal, 81 (1995), 55-65.
doi: 10.1215/S0012-7094-95-08106-X. |
[32] |
F. J. Martínez de Albéniz, M. Núñez and C. Rafels, Assignment markets with the same core, Games and Economic Behavior, 73 (2011), 553-563.
doi: 10.1016/j.geb.2011.02.011. |
[33] |
F. J. Martínez de Albéniz, C. Rafels and N. Ybern, On the nucleolus of 2x2 assignment games, Economics Bulletin 3 (2013), 2938-2947. |
[34] |
F. J. Martínez de Albéniz, C. Rafels and N. Ybern, A procedure to compute the nucleolus of the assignment game, Operations Research Letters 41 (2013), 675-678. |
[35] |
F. J. Martínez de Albéniz and C. Rafels, Cooperative assignment games with the inverse Monge property, Discrete Applied Mathematics, 162 (2014), 42-50.
doi: 10.1016/j.dam.2013.08.027. |
[36] |
M. Maschler, B. Peleg and L. S. Shapley, Geometric properties of the kernel, nucleolus and related solution concepts, Mathematics of Operations Research, 4 (1979), 303-338.
doi: 10.1287/moor.4.4.303. |
[37] |
J. Massó and A. Neme, On cooperative solutions of a generalized assignment game: Limit theorems to the set of competitive equilibria, Journal of Economic Theory, 154 (2014), 187-215.
doi: 10.1016/j.jet.2014.09.016. |
[38] |
J. P. Mo, Entry and structures of interest groups in assignment games, Journal of Economic Theory, 46 (1988), 66-96.
doi: 10.1016/0022-0531(88)90150-0. |
[39] |
M. Núñez, A note on the nucleolus and the kernel of the assignment game, International Journal of Game Theory, 33 (2004), 55-65.
doi: 10.1007/s001820400184. |
[40] |
M. Núñez and C. Rafels, Buyer-seller exactness in the assignment game, International Journal of Game Theory, 31 (2002), 423-436.
doi: 10.1007/s001820300128. |
[41] |
M. Núñez and C. Rafels, The assignment game: the $\tau$-value, International Journal of Game Theory, 31 (2002), 411-422.
doi: 10.1007/s001820300127. |
[42] |
M. Núñez and C. Rafels, Characterization of the extreme core allocations of the assignment game, Games and Economic Behavior, 44 (2003), 311-331.
doi: 10.1016/S0899-8256(03)00054-X. |
[43] |
M. Núñez and C. Rafels, On the dimension of the core of the assignment game, Games and Economic Behavior, 64 (2008), 290-302.
doi: 10.1016/j.geb.2008.01.004. |
[44] |
M. Núñez and C. Rafels, A glove-market partitioned matrix related to the assignment game, Games and Economic Behavior, 67 (2009), 598-610.
doi: 10.1016/j.geb.2009.03.014. |
[45] |
M. Núñez and C. Rafels, Von Neumann-Morgenstern solutions in the assignment market, Journal of Economic Theory, 148 (2013), 1282-1291.
doi: 10.1016/j.jet.2012.10.002. |
[46] |
M. Núñez and T. Solymosi, Lexicographic allocations and extreme core payoffs: The case of assignment games, Corvinus Economics Working Papers, CEWP 15/2014 (2014). |
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G. Owen, The Assignment Game: The Reduced Game, Annales d'Économie et de Statistique, (1992), 71-79. |
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B. Peleg, On the reduced game property and its converse, International Journal of Game Theory, 15 (1986), 187-200.
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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. |
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D. Pérez-Castrillo and M. Sotomayor, On the manipulability of competitive equilibrium rules in many-to-many buyer-seller markets, Working paper, 2014. |
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T. Quint, Characterization of cores of assignment games, International Journal of Game Theory, 19 (1991), 413-420.
doi: 10.1007/BF01766430. |
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T. Quint, The core of an m-sided assignment game, Games and Economic Behavior, 3 (1991), 487-503.
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show all references
References:
[1] |
R. P. Arribillaga, J. Massó and A. Neme, On the structure of cooperative and competitive solutions of a generalized assignment game, Journal of Applied Mathematics, (2014), Art. ID 190614, 20 pp.
doi: 10.1155/2014/190614. |
[2] |
L. M. Ausubel and P. Milgrom, Ascending auctions with package bidding, Frontiers of Theoretical Economics, 1 (2002), 44pp(Republished in BePress Advances in Theoretical Economics).
doi: 10.2202/1534-5955.1019. |
[3] |
L. M. Ausubel and P. Milgrom, The lovely but lonely Vickrey auction, In Combinatorial Auctions (ed. P. Cramton, R. Steinberg and Y. Shoham), MIT Press, 2005. |
[4] |
L. M. Ausubel and P. Milgrom, Ascending Proxy Auctions, In Combinatorial Auctions (ed. P. Cramton, R. Steinberg and Y. Shoham), MIT Press, 2005. |
[5] |
M. L. Balinski and D. Gale, On the core of the assignment game, In Functional Analysis, Optimization and Mathematical Economics (ed. L.J. Leifman), Oxford University (1990), 274-289. |
[6] |
S. Bikhchandani and J. M. Ostroy, The package assignment model, Journal of Economic Theory, 107 (2002), 377-406.
doi: 10.1006/jeth.2001.2957. |
[7] |
G. Birkhoff, Tres observaciones sobre el álgebra lineal, Revista Universidad Nacional de Tucuman, Series A, 5 (1946), 147-151. |
[8] |
R. van den Brink and M. Pintér, On axiomatizations of the Shapley value for assignment games, Journal of Mathematical Economics, 60 (2015), 110-114.
doi: 10.1016/j.jmateco.2015.06.016. |
[9] |
E. Camiña, A generalized assignment game, Mathematical Social Sciences, 52 (2006), 152-161.
doi: 10.1016/j.mathsocsci.2006.06.003. |
[10] |
V. P. Crawford and E. M. Knoer, Job matching with heterogeneous firms and workers, Econometrica, 49 (1981), 437-450.
doi: 10.2307/1913320. |
[11] |
M. Davis and M. Maschler, The kernel of a cooperative game, Naval Research Logistics Quarterly 12 (1965), 223-259.
doi: 10.1002/nav.3800120303. |
[12] |
G. Demange, Strategyproofness in the Assignment Market Game, Laboratoire d'Econometrie de l'Ecole Polytechnique, Paris, Mimeo, 1982. |
[13] |
G. Demange and D. Gale, The strategy structure of two-sided matching markets, Econometrica, 53 (1985), 873-888.
doi: 10.2307/1912658. |
[14] |
G. Demange, D. Gale and M. Sotomayor, Multi-item auctions, Journal of Political Economy, 94 (1986), 863-872.
doi: 10.1086/261411. |
[15] |
T. S. H. Driessen, A note on the inclusion of the kernel in the core of the bilateral assignment game, International Journal of Game Theory, 27 (1998), 301-303.
doi: 10.1007/s001820050073. |
[16] |
A. Fagebaume, D. Gale and M. Sotomayor, A note on the multiple-partners assignment game, Journal of Mathematical Economics, 46 (2010), 388-392.
doi: 10.1016/j.jmateco.2009.06.014. |
[17] |
D. Gale, The Theory of Linear Economic Models, McGraw-Hill, New York, 1960. |
[18] |
D. Gale and L. S. Shapley, College Admission and the Stability of Marriage, American Mathematical Monthly, 69 (1962), 9-15.
doi: 10.2307/2312726. |
[19] |
H. Hamers, F. Klijn, T. Solymosi, S. Tijs and J. P. Villar, Assignment games satisfy the CoMa-property, Games and Economic Behavior, 38 (2002), 231-239. |
[20] |
M. Hoffmann and P. Sudhölter, The Shapley value of exact assignment games, International Journal of Game Theory 35 (2007), 557-568.
doi: 10.1007/s00182-006-0068-8. |
[21] |
J. M. Izquierdo, M. Núñez and C. Rafels, A simple procedure to obtain the extreme core allocations of an assignment market, International Journal of Game Theory, 36 (2007), 17-26.
doi: 10.1007/s00182-007-0091-4. |
[22] |
D. Jaume, J. Massó and A. Neme, The multiple-partners assignment game with heterogeneous sales and multi-unit demands: competitive equilibria, Mathematical Methods of Operations Research, 76 (2012), 161-187.
doi: 10.1007/s00186-012-0395-4. |
[23] |
M. Kaneko, On the core and competitive equilibria of a market with indivisible goods, Naval Research Logistics Quarterly, 23 (1976), 321-337.
doi: 10.1002/nav.3800230214. |
[24] |
M. Kaneko, The central assignment game and the assignment markets, Journal of Mathematical Economics, 10 (1982), 205-232.
doi: 10.1016/0304-4068(82)90038-6. |
[25] |
M. Kaneko and M. Wooders, Cores of partitioning games, Mathematical Social Sciences, 3 (1982), 313-327.
doi: 10.1016/0165-4896(82)90015-4. |
[26] |
T. C. Koopmans and M. Beckmann, Assignment Problems and the Location of Economic Activities, Econometrica, 25 (1957), 53-76.
doi: 10.2307/1907742. |
[27] |
H. B. Leonard, Elicitation of honest preferences for the assignment of individuals to positions, Journal of Political Economy, 91 (1983), 461-479.
doi: 10.1086/261158. |
[28] |
F. Llerena and M. Núñez, A geometric characterization of the nucleolus of the assignment game, Economics Bulletin 31 (2011), 3275-3285. |
[29] |
F. Llerena, M. Núñez and C. Rafels, An axiomatization of the nucleolus of the assignment game, International Journal of Game Theory, 44 (2015), 1-15.
doi: 10.1007/s00182-014-0416-z. |
[30] |
W. F. Lucas, A game with no solution, Bulletin of the American Mathematical Society, 74 (1968), 237-239.
doi: 10.1090/S0002-9904-1968-11901-9. |
[31] |
W. F. Lucas, Core theory for multiple-sided assignment games, Duke Mathematical Journal, 81 (1995), 55-65.
doi: 10.1215/S0012-7094-95-08106-X. |
[32] |
F. J. Martínez de Albéniz, M. Núñez and C. Rafels, Assignment markets with the same core, Games and Economic Behavior, 73 (2011), 553-563.
doi: 10.1016/j.geb.2011.02.011. |
[33] |
F. J. Martínez de Albéniz, C. Rafels and N. Ybern, On the nucleolus of 2x2 assignment games, Economics Bulletin 3 (2013), 2938-2947. |
[34] |
F. J. Martínez de Albéniz, C. Rafels and N. Ybern, A procedure to compute the nucleolus of the assignment game, Operations Research Letters 41 (2013), 675-678. |
[35] |
F. J. Martínez de Albéniz and C. Rafels, Cooperative assignment games with the inverse Monge property, Discrete Applied Mathematics, 162 (2014), 42-50.
doi: 10.1016/j.dam.2013.08.027. |
[36] |
M. Maschler, B. Peleg and L. S. Shapley, Geometric properties of the kernel, nucleolus and related solution concepts, Mathematics of Operations Research, 4 (1979), 303-338.
doi: 10.1287/moor.4.4.303. |
[37] |
J. Massó and A. Neme, On cooperative solutions of a generalized assignment game: Limit theorems to the set of competitive equilibria, Journal of Economic Theory, 154 (2014), 187-215.
doi: 10.1016/j.jet.2014.09.016. |
[38] |
J. P. Mo, Entry and structures of interest groups in assignment games, Journal of Economic Theory, 46 (1988), 66-96.
doi: 10.1016/0022-0531(88)90150-0. |
[39] |
M. Núñez, A note on the nucleolus and the kernel of the assignment game, International Journal of Game Theory, 33 (2004), 55-65.
doi: 10.1007/s001820400184. |
[40] |
M. Núñez and C. Rafels, Buyer-seller exactness in the assignment game, International Journal of Game Theory, 31 (2002), 423-436.
doi: 10.1007/s001820300128. |
[41] |
M. Núñez and C. Rafels, The assignment game: the $\tau$-value, International Journal of Game Theory, 31 (2002), 411-422.
doi: 10.1007/s001820300127. |
[42] |
M. Núñez and C. Rafels, Characterization of the extreme core allocations of the assignment game, Games and Economic Behavior, 44 (2003), 311-331.
doi: 10.1016/S0899-8256(03)00054-X. |
[43] |
M. Núñez and C. Rafels, On the dimension of the core of the assignment game, Games and Economic Behavior, 64 (2008), 290-302.
doi: 10.1016/j.geb.2008.01.004. |
[44] |
M. Núñez and C. Rafels, A glove-market partitioned matrix related to the assignment game, Games and Economic Behavior, 67 (2009), 598-610.
doi: 10.1016/j.geb.2009.03.014. |
[45] |
M. Núñez and C. Rafels, Von Neumann-Morgenstern solutions in the assignment market, Journal of Economic Theory, 148 (2013), 1282-1291.
doi: 10.1016/j.jet.2012.10.002. |
[46] |
M. Núñez and T. Solymosi, Lexicographic allocations and extreme core payoffs: The case of assignment games, Corvinus Economics Working Papers, CEWP 15/2014 (2014). |
[47] |
G. Owen, The Assignment Game: The Reduced Game, Annales d'Économie et de Statistique, (1992), 71-79. |
[48] |
B. Peleg, On the reduced game property and its converse, International Journal of Game Theory, 15 (1986), 187-200.
doi: 10.1007/BF01769258. |
[49] |
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. |
[50] |
D. Pérez-Castrillo and M. Sotomayor, On the manipulability of competitive equilibrium rules in many-to-many buyer-seller markets, Working paper, 2014. |
[51] |
T. Quint, Characterization of cores of assignment games, International Journal of Game Theory, 19 (1991), 413-420.
doi: 10.1007/BF01766430. |
[52] |
T. Quint, The core of an m-sided assignment game, Games and Economic Behavior, 3 (1991), 487-503.
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