# American Institute of Mathematical Sciences

April  2015, 2(3&4): 227-256. doi: 10.3934/jdg.2015003

## A survey on assignment markets

 1 Departament de Matemàtica Econòmica, Financera i Actuarial, Universitat de Barcelona, Av. Diagonal, 690, 08034 Barcelona, Spain, Spain

Received  December 2014 Revised  January 2015 Published  November 2015

The assignment game is a two-sided market, say buyers and sellers, where demand and supply are unitary and utility is transferable by means of prices. This survey is structured in three parts: a first part, from the introduction of the assignment game by Shapley and Shubik (1972) until the publication of the book of Roth and Sotomayor (1990), focused on the notion of core; the subsequent investigations that broaden the scope to other notions of solution for these markets; and its extensions to assignment markets with multiple sides or multiple partnership. These extended two-sided assignment markets, that allow for multiple partnership, better represent the situation in a labour market or an auction.
Citation: Marina Núñez, Carles Rafels. A survey on assignment markets. Journal of Dynamics & Games, 2015, 2 (3&4) : 227-256. doi: 10.3934/jdg.2015003
##### References:
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Lucas, Core theory for multiple-sided assignment games, Duke Mathematical Journal, 81 (1995), 55-65. doi: 10.1215/S0012-7094-95-08106-X.  Google Scholar [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.  Google Scholar [33] F. J. Martínez de Albéniz, C. Rafels and N. Ybern, On the nucleolus of 2x2 assignment games, Economics Bulletin 3 (2013), 2938-2947. Google Scholar [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. Google Scholar [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.  Google Scholar [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.  Google Scholar [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.  Google Scholar [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.  Google Scholar [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.  Google Scholar [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.  Google Scholar [41] M. Núñez and C. 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