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Monge assignment games

Author

Listed:
  • 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.

Suggested Citation

  • F. Javier Martinez de Albeniz & Carles Rafels, 2012. "Monge assignment games," Working Papers in Economics 282, Universitat de Barcelona. Espai de Recerca en Economia.
    • Handle: RePEc:bar:bedcje:2012282
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    References listed on IDEAS

    as
    1. Burkard, Rainer E., 2007. "Monge properties, discrete convexity and applications," European Journal of Operational Research, Elsevier, vol. 176(1), pages 1-14, January.
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    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 461-479, June.
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    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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