Monge assignment games
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.
|Date of creation:||2012|
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- Perez-Castrillo, David & Sotomayor, Marilda, 2002.
"A Simple Selling and Buying Procedure,"
Journal of Economic Theory,
Elsevier, vol. 103(2), pages 461-474, April.
- Perez-Castrillo, D. & Sotomayor, M., 1998. "A Simple Selling and Buying Procedure," UFAE and IAE Working Papers 421.98, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- David Perez-Castrillo & Marilda Sotomayor, 2000. "A Simple Selling and Buying Procedure," Econometric Society World Congress 2000 Contributed Papers 0704, Econometric Society.
- 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 461-479, June.
- Becker, Gary S, 1973. "A Theory of Marriage: Part I," Journal of Political Economy, University of Chicago Press, vol. 81(4), pages 813-846, July-Aug..
- Burkard, Rainer E., 2007. "Monge properties, discrete convexity and applications," European Journal of Operational Research, Elsevier, vol. 176(1), pages 1-14, January.
- Demange, Gabrielle & Gale, David & Sotomayor, Marilda, 1986. "Multi-Item Auctions," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 863-872, August.
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