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Balancedness Conditions for Exact Games

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Author Info

  • Péter Csóka

    ()
    (Department of Economics, Maastricht University)

  • P. Jean-Jacques Herings

    ()
    (Department of Economics, Maastricht University)

  • László Á. Kóczy

    ()
    (Budapest Tech)

Abstract

We provide two new characterizations of exact games. First, a game is exact if and only if it is exactly balanced; and second, a game is exact if and only if it is totally balanced and overbalanced. The condition of exact balancedness is identical to the one of balancedness, except that one of the balancing weights may be negative while for overbalancedness one of the balancing weights is required to be non-positive and no weight is put on the grand coalition. Exact balancedness and overbalancedness are both easy to formulate conditions with a natural game-theoretic interpretation and are shown to be useful in applications. Using exact balancedness we show that exact games are convex for the grand coalition and we provide an alternative proof that the classes of convex and totally exact games coincide. We provide an example of a game that is totally balanced and convex for the grand coalition,but not exact. Finally we relate classes of balanced, totally balanced, convex for the grand coalition, exact, totally exact, and convex games to one another.

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File URL: http://uni-obuda.hu/users/vecseya/RePEc/pkk/wpaper/0805.pdf
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Bibliographic Info

Paper provided by Óbuda University, Keleti Faculty of Business and Management in its series Working Paper Series with number 0805.

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Length: 13 pages
Date of creation: Sep 2007
Date of revision: May 2008
Handle: RePEc:pkk:wpaper:0805

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Keywords: Totally Balanced Games; Exact Games; Convex Games;

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References

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  1. Velzen, S. van & Hamers, H.J.M. & Solymosi, T., 2004. "Core Stability in Chain-Component Additive Games," Discussion Paper 2004-101, Tilburg University, Center for Economic Research.
  2. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, vol. 1(1), pages 9-25, June.
  3. Predtetchinski, Arkadi & Jean-Jacques Herings, P., 2004. "A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game," Journal of Economic Theory, Elsevier, vol. 116(1), pages 84-92, May.
  4. Legut, Jerzy, 1990. "On totally balanced games arising from cooperation in fair division," Games and Economic Behavior, Elsevier, vol. 2(1), pages 47-60, March.
  5. Yaron Azrieli & Ehud Lehrer, 2004. "On Concavification and Convex Games," Game Theory and Information 0408002, EconWPA.
  6. Peter Csoka & P. Jean-Jacques Herings, & Laszlo A. Koczy, 2007. "Stable Allocations of Risk," IEHAS Discussion Papers 0704, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
  7. Csóka Péter & Herings P. Jean-Jacques & Kóczy László Á. & Pintér Miklós, 2009. "Convex and Exact Games with Non-transferable Utility," Research Memorandum 031, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  8. Ehud Kalai & Eitan Zemel, 1980. "Generalized Network Problems Yielding Totally Balanced Games," Discussion Papers 425, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  9. Casas-Mendez, Balbina & Garcia-Jurado, Ignacio & van den Nouweland, Anne & Vazquez-Brage, Margarita, 2003. "An extension of the [tau]-value to games with coalition structures," European Journal of Operational Research, Elsevier, vol. 148(3), pages 494-513, August.
  10. Branzei, R. & Tijs, S. & Zarzuelo, J., 2009. "Convex multi-choice games: Characterizations and monotonic allocation schemes," European Journal of Operational Research, Elsevier, vol. 198(2), pages 571-575, October.
  11. Calleja, Pedro & Borm, Peter & Hendrickx, Ruud, 2005. "Multi-issue allocation situations," European Journal of Operational Research, Elsevier, vol. 164(3), pages 730-747, August.
  12. Tijs, S.H. & Parthasarathy, T. & Potters, J.A.M. & Rajendra Prasad, V., 1984. "Permutation games: Another class of totally balanced games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154278, Tilburg University.
  13. Biswas, A. K. & Parthasarathy, T. & Potters, J. A. M. & Voorneveld, M., 1999. "Large Cores and Exactness," Games and Economic Behavior, Elsevier, vol. 28(1), pages 1-12, July.
  14. Ehud Kalai & Eitan Zemel, 1980. "On Totally Balanced Games and Games of Flow," Discussion Papers 413, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  15. Hans Reijnierse & Jean Derks, 1998. "Note On the core of a collection of coalitions," International Journal of Game Theory, Springer, vol. 27(3), pages 451-459.
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Citations

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Cited by:
  1. Lohmann E. & Borm P. & Herings P.J.J., 2011. "Minimal exact balancedness," Research Memorandum 009, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  2. Estévez-Fernández, Arantza, 2012. "New characterizations for largeness of the core," Games and Economic Behavior, Elsevier, vol. 76(1), pages 160-180.
  3. Michel Grabisch & Peter Sudhölter, 2014. "On the restricted cores and the bounded core of games on distributive lattices," PSE - Labex "OSE-Ouvrir la Science Economique" halshs-00950109, HAL.
  4. Péter Csóka & P. Jean-Jacques Herings & László Á. Kóczy, 2007. "Stable Allocations of Risk," Working Paper Series 0802, Óbuda University, Keleti Faculty of Business and Management, revised Apr 2008.
  5. Arantza Estevez-Fernandez, 2011. "New Characterizations for Largeness of the Core," Tinbergen Institute Discussion Papers 11-086/1, Tinbergen Institute.

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