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On the bargaining set, kernel and core of superadditive games

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Author Info

  • TamÂs Solymosi

    ()
    (Department of Operations Research, Budapest University of Economic Sciences, 1828 Budapest, Pf. 489, Hungary)

Abstract

We prove that for superadditive games a necessary and sufficient condition for the bargaining set to coincide with the core is that the monotonic cover of the excess game induced by a payoff be balanced for each imputation in the bargaining set. We present some new results obtained by verifying this condition for specific classes of games. For N-zero-monotonic games we show that the same condition required at each kernel element is also necessary and sufficient for the kernel to be contained in the core. We also give examples showing that to maintain these characterizations, the respective assumptions on the games cannot be lifted.

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Bibliographic Info

Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 28 (1999)
Issue (Month): 2 ()
Pages: 229-240

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Handle: RePEc:spr:jogath:v:28:y:1999:i:2:p:229-240

Note: Received: March 1998/Revised version: December 1998
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Related research

Keywords: Cooperative games · bargaining set · core · kernel;

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Cited by:
  1. Marina Nunez Oliva & Carlos Rafels Pallarola, 2001. "The extreme core allocations of the assignment game," Working Papers in Economics 65, Universitat de Barcelona. Espai de Recerca en Economia.
  2. Drechsel, J. & Kimms, A., 2010. "Computing core allocations in cooperative games with an application to cooperative procurement," International Journal of Production Economics, Elsevier, vol. 128(1), pages 310-321, November.
  3. Grahn, Sofia, 2001. "Core and Bargaining Set of Shortest Path Games," Working Paper Series 2001:3, Uppsala University, Department of Economics.
  4. Daniel Granot, 2010. "The reactive bargaining set for cooperative games," International Journal of Game Theory, Springer, vol. 39(1), pages 163-170, March.
  5. Josep M Izquierdo & Carles Rafels, 2012. "On the coincidence of the core and the bargaining sets," Economics Bulletin, AccessEcon, vol. 32(3), pages 2035-2043.
  6. Peter Sudhölter & Jos A. M. Potters, 2001. "The semireactive bargaining set of a cooperative game," International Journal of Game Theory, Springer, vol. 30(1), pages 117-139.
  7. Hendrickx, R.L.P. & Borm, P.E.M. & Timmer, J.B., 2000. "On Convexity for NTU-Games," Discussion Paper 2000-108, Tilburg University, Center for Economic Research.
  8. Josep M. Izquierdo & Carles Rafels, 2010. "On the coincidence between the Shimomuras bargaining sets and the core," Working Papers in Economics 241, Universitat de Barcelona. Espai de Recerca en Economia.
  9. Massimiliano Amarante & Luigi Montrucchio, 2007. "Mas-Colell Bargaining Set of Large Games," Carlo Alberto Notebooks 63, Collegio Carlo Alberto.
  10. Massimiliano Amarante & Luigi Montrucchio, 2010. "The bargaining set of a large game," Economic Theory, Springer, vol. 43(3), pages 313-349, June.
  11. Tamás Solymosi, 2008. "Bargaining sets and the core in partitioning games," Central European Journal of Operations Research, Springer, vol. 16(4), pages 425-440, December.
  12. Josep Maria Izquierdo Aznar & Carlos Rafels Pallarola, 2002. "Coalitionally Monotonic Set-solutions for Cooperative TU Games," Working Papers in Economics 75, Universitat de Barcelona. Espai de Recerca en Economia.

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