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Assignment markets that are uniquely determined by their core

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  • Javier Martínez-de-Albéniz, F.
  • Núñez, Marina
  • Rafels, Carles

Abstract

A matrix A defines an assignment market, 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. Quint (1991) points out that usually many different assignment matrices exist that define markets with the same core and poses the question of when the matrix is uniquely determined by the core of the related market. We characterize these matrices in terms of a strong form of the doubly dominant diagonal property. A matching between buyers and sellers is optimal if it produces the maximum units of utility. Our characterization allows us to show that the number of optimal matchings in markets uniquely characterized by their core is a power of two.

Suggested Citation

  • Javier Martínez-de-Albéniz, F. & Núñez, Marina & Rafels, Carles, 2011. "Assignment markets that are uniquely determined by their core," European Journal of Operational Research, Elsevier, vol. 212(3), pages 529-534, August.
    • Handle: RePEc:eee:ejores:v:212:y:2011:i:3:p:529-534
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    References listed on IDEAS

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    1. Meca, Ana & Timmer, Judith & Garcia-Jurado, Ignacio & Borm, Peter, 2004. "Inventory games," European Journal of Operational Research, Elsevier, vol. 156(1), pages 127-139, July.
      • Meca-Martinez, A. & Timmer, J.B. & Garcia-Jurado, I. & Borm, P.E.M., 1999. "Inventory Games," Other publications TiSEM 21f26b3f-7fae-4f19-908f-a, Tilburg University, School of Economics and Management.
      • Meca, A. & Timmer, J.B. & Garcia-Jurado, I. & Borm, P.E.M., 2004. "Inventory games," Other publications TiSEM 49368f2d-02fc-49c9-9d74-8, Tilburg University, School of Economics and Management.
      • Meca-Martinez, A. & Timmer, J.B. & Garcia-Jurado, I. & Borm, P.E.M., 1999. "Inventory Games," Discussion Paper 1999-53, Tilburg University, Center for Economic Research.
    2. Peter Borm & Herbert Hamers & Ruud Hendrickx, 2001. "Operations research games: A survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 139-199, December.
    3. Nagarajan, Mahesh & Sosic, Greys, 2008. "Game-theoretic analysis of cooperation among supply chain agents: Review and extensions," European Journal of Operational Research, Elsevier, vol. 187(3), pages 719-745, June.
    4. Quint, Thomas, 1991. "Characterization of Cores of Assignment Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(4), pages 413-420.
    5. T. E. S. Raghavan & Tamás Solymosi, 2001. "Assignment games with stable core," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 177-185.
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    Cited by:

    1. F.Javier Martínez-de-Albéniz & Carles Rafels & Neus Ybern, 2015. "Insights into the nucleolus of the assignment game," UB School of Economics Working Papers 2015/333, University of Barcelona School of Economics.

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