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Assignment markets with the same core

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

Abstract

In the framework of bilateral assignment games, we study the set of matrices associated with assignment markets with the same core. We state conditions on matrix entries that ensure that the related assignment games have the same core. We prove that the set of matrices leading to the same core form a join-semilattice with a finite number of minimal elements and a unique maximum. We provide a characterization of the minimal elements. A sufficient condition under which the join-semilattice reduces to a lattice is also given.

Suggested Citation

  • Martínez-de-Albéniz, F. Javier & Núñez, Marina & Rafels, Carles, 2011. "Assignment markets with the same core," Games and Economic Behavior, Elsevier, vol. 73(2), pages 553-563.
  • Handle: RePEc:eee:gamebe:v:73:y:2011:i:2:p:553-563 DOI: 10.1016/j.geb.2011.02.011
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    References listed on IDEAS

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    1. Marina Núñez, 2004. "A note on the nucleolus and the kernel of the assignment game," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(1), pages 55-65, January.
    2. Josep Izquierdo & Marina Núñez & Carles Rafels, 2007. "A simple procedure to obtain the extreme core allocations of an assignment market," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(1), pages 17-26, September.
    3. Solymosi, Tamas & Raghavan, Tirukkannamangai E S, 1994. "An Algorithm for Finding the Nucleolus of Asignment Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(2), pages 119-143.
    4. Hamers, Herbert & Klijn, Flip & Solymosi, Tamas & Tijs, Stef & Pere Villar, Joan, 2002. "Assignment Games Satisfy the CoMa-Property," Games and Economic Behavior, Elsevier, vol. 38(2), pages 231-239, February.
    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.
    6. Núñez, Marina & Rafels, Carles, 2008. "On the dimension of the core of the assignment game," Games and Economic Behavior, Elsevier, vol. 64(1), pages 290-302, September.
    7. Nunez, Marina & Rafels, Carles, 2003. "Characterization of the extreme core allocations of the assignment game," Games and Economic Behavior, Elsevier, vol. 44(2), pages 311-331, August.
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    Cited by:

    1. Tejada, J. & Borm, P.E.M. & Lohmann, E.R.M.A., 2013. "A Unifying Model for Matching Situations," Discussion Paper 2013-069, Tilburg University, Center for Economic Research.
    2. Nunez, Marina & Solymosi, Tamás, 2014. "Lexicographic allocations and extreme core payoffs: the case of assignment games," Corvinus Economics Working Papers (CEWP) 2014/15, Corvinus University of Budapest.
    3. F.Javier Martínez-de-Albéniz & Carles Rafels & Neus Ybern, 2015. "Insights into the nucleolus of the assignment game," UB Economics Working Papers 2015/333, Universitat de Barcelona, Facultat d'Economia i Empresa, UB Economics.
    4. Tejada, O. & Borm, P. & Lohmann, E., 2014. "A unifying model for matrix-based pairing situations," Mathematical Social Sciences, Elsevier, vol. 72(C), pages 55-61.

    More about this item

    Keywords

    Assignment game; Core; Semilattice;

    JEL classification:

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

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