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A glove-market partitioned matrix related to the assignment game

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  • Núñez, Marina
  • Rafels, Carles

Abstract

To any assignment market we associate the unique exact assignment game defined on the same set of agents and with a core that is a translation of the core of the initial market. As it happens with the core, the kernel and the nucleolus of an assignment game are proved to be the translation of the kernel and the nucleolus of its related exact assignment game by the vector of minimum core payoffs. Agents on each side of the market are classified by means of an equivalence relation and, when agents on the same class are ordered to be consecutive, the related exact assignment market is defined by a partitioned matrix, each block of the partition being a glove market.

Suggested Citation

  • Núñez, Marina & Rafels, Carles, 2009. "A glove-market partitioned matrix related to the assignment game," Games and Economic Behavior, Elsevier, vol. 67(2), pages 598-610, November.
    • Handle: RePEc:eee:gamebe:v:67:y:2009:i:2:p:598-610
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    References listed on IDEAS

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    1. Maike Hoffmann & Peter Sudhölter, 2007. "The Shapley value of exact assignment games," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(4), pages 557-568, April.
    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.
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    4. Marina Núñez & Carles Rafels, 2005. "The Böhm–Bawerk horse market: a cooperative analysis," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(3), pages 421-430, September.
    5. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Theo S. H. Driessen, 1998. "A note on the inclusion of the kernel in the core of the bilateral assignment game," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(2), pages 301-303.
    7. M. Maschler & B. Peleg & L. S. Shapley, 1979. "Geometric Properties of the Kernel, Nucleolus, and Related Solution Concepts," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 303-338, November.
    8. 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.
    9. 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.
    10. 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.
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    Cited by:

    1. Núñez, Marina & Rafels, Carles, 2013. "Von Neumann–Morgenstern solutions in the assignment market," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1282-1291.
    2. Marina Núñez & Carles Rafels, 2009. "Von Neumann-Morgenstern stable-set solutions in the assignment market," Working Papers 412, Barcelona School of Economics.
    3. Hirai, Toshiyuki & Watanabe, Naoki, 2018. "von Neumann–Morgenstern stable sets of a patent licensing game: The existence proof," Mathematical Social Sciences, Elsevier, vol. 94(C), pages 1-12.

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