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A note on the inclusion of the kernel in the core of the bilateral assignment game

Author

Listed:
  • Theo S. H. Driessen

    () (Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands)

Abstract

In this note we prove that the kernel of a bilateral assignment game is always included in the core. This solves an outstanding open problem for bilateral assignment games.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:jogath:v:27:y:1998:i:2:p:301-303 Note: Received January 1997/Final version June 1997
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    References listed on IDEAS

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    1. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer;Game Theory Society, pages 89-99.
    2. Andrzej S. Nowak, 1997. "note: On an Axiomatization of the Banzhaf Value without the Additivity Axiom," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(1), pages 137-141.
    3. Haller, Hans, 1994. "Collusion Properties of Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(3), pages 261-281.
    4. Nowak, A.S. & Radzik, T., 1995. "On axiomatizations of the weighted Shapley values," Games and Economic Behavior, Elsevier, vol. 8(2), pages 389-405.
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    Citations

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    Cited by:

    1. Marina Nunez Oliva & Carlos Rafels Pallarola, 2005. "Uniform-price assignment markets," Working Papers in Economics 135, Universitat de Barcelona. Espai de Recerca en Economia.
    2. Oriol Tejada & Carles Rafels, 2009. "Symmetrically multilateral-bargained allocations in multi-sided assignment markets," Working Papers in Economics 216, Universitat de Barcelona. Espai de Recerca en Economia.
    3. Jun Wako, 2006. "Another proof that assignment games have singleton cores only if multiple optimal matchings exist," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 213-217.
    4. Bolle, Friedel & Breitmoser, Yves & Otto, Philipp E., 2011. "A positive theory of cooperative games: The logit core and its variants," MPRA Paper 32918, University Library of Munich, Germany.
    5. 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.
    6. Adegbesan, Tunji, 2007. "Strategic factor markets: Bargaining, scarcity, and resource complementarity," IESE Research Papers D/666, IESE Business School.

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