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Monge assignment games

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  • F. Javier Martinez de Albeniz
  • Carles Rafels

    (Universitat de Barcelona)

Abstract

An assignment game is defined by a matrix A, where each row represents a buyer and each column a seller. If buyer i is matched with seller j, the market produces aij units of utility. We study Monge assignment games, that is bilateral cooperative assignment games where the assignment matrix satisfies the Monge property. These matrices can be characterized by the fact that in any submatrix of 2 2 an optimal matching is placed in its main diagonal. For square markets, we describe their cores by using only the central tridiagonal band of the elements of the matrix. We obtain a closed formula for the buyers-optimal and the sellers-optimal core allocations. Non- square markets are analyzed also by reducing them to appropriate square matrices.

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Bibliographic Info

Paper provided by Universitat de Barcelona. Espai de Recerca en Economia in its series Working Papers in Economics with number 282.

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Length: 0 pages
Date of creation: 2012
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Handle: RePEc:bar:bedcje:2012282

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Postal: Espai de Recerca en Economia, Facultat de Ciències Econòmiques. Tinent Coronel Valenzuela, Num 1-11 08034 Barcelona. Spain.
Web page: http://www.ere.ub.es
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  1. David Perez-Castrillo & Marilda Sotomayor, 2000. "A Simple Selling and Buying Procedure," Econometric Society World Congress 2000 Contributed Papers 0704, Econometric Society.
  2. Demange, Gabrielle & Gale, David & Sotomayor, Marilda, 1986. "Multi-Item Auctions," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 863-72, August.
  3. Becker, Gary S, 1973. "A Theory of Marriage: Part I," Journal of Political Economy, University of Chicago Press, vol. 81(4), pages 813-46, July-Aug..
  4. Burkard, Rainer E., 2007. "Monge properties, discrete convexity and applications," European Journal of Operational Research, Elsevier, vol. 176(1), pages 1-14, January.
  5. Leonard, Herman B, 1983. "Elicitation of Honest Preferences for the Assignment of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 461-79, June.
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