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Convex and Exact Games with Non-transferable Utility

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Author Info

  • Péter Csóka

    ()
    (Department of Finance, Corvinus University of Budapest)

  • P. Jean-Jacques Herings

    ()
    (Department of Economics, Maastricht University)

  • László Á. Kóczy

    ()
    (Keleti Faculty of Economics, Budapest Tech and Department of Economics, Maastricht University)

  • Miklós Pintér

    ()
    (Department of Mathematics, Corvinus University of Budapest)

Abstract

We generalize exactness to games with non-transferable utility (NTU). In an exact game for each coalition there is a core allocation on the boundary of its payoff set. Convex games with transferable utility are well-known to be exact. We study five generalizations of convexity in the NTU setting. We show that each of ordinal, coalition merge, individual merge and marginal convexity can be unified under NTU exactness. We provide an example of a cardinally convex game which is not NTU exact. Finally, we relate the classes of \Pi-balanced, totally \Pi-balanced, NTU exact, totally NTU exact, ordinally convex, cardinally convex, coalition merge convex, individual merge convex and marginal convex games to one another.

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File URL: http://uni-obuda.hu/users/vecseya/RePEc/pkk/wpaper/0904.pdf
File Function: Manuscript, 2009
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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 0904.

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Length: 18 pages
Date of creation: Jun 2009
Date of revision:
Handle: RePEc:pkk:wpaper:0904

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Keywords: NTU Games; Exact Games; Convex Games;

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  3. Hendrickx, R.L.P. & Borm, P.E.M. & Timmer, J.B., 2002. "A note on NTU-convexity," Open Access publications from Tilburg University urn:nbn:nl:ui:12-90186, Tilburg University.
  4. Peleg, Bezalel, 1986. "A proof that the core of an ordinal convex game is a von Neumann-Morgenstern solution," Mathematical Social Sciences, Elsevier, vol. 11(1), pages 83-87, February.
  5. Herings,P. Jean-Jacques & Predtetchinski,Arkadi, 2002. "A Necessary and Sufficient Condition for Non--emptiness of the Core of a Non--transferable Utility Game," Research Memorandum 016, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  6. 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.
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  8. 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.
  9. Granot, D, et al, 1996. "The Kernel/Nucleolus of a Standard Tree Game," International Journal of Game Theory, Springer, vol. 25(2), pages 219-44.
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  13. Pulido, Manuel A. & Sánchez-Soriano, Joaquín, 2009. "On the core, the Weber set and convexity in games with a priori unions," European Journal of Operational Research, Elsevier, vol. 193(2), pages 468-475, March.
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Citations

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Cited by:
  1. Csóka, Péter & Herings, P. Jean-Jacques & Kóczy, László Á., 2007. "Balancedness Conditions for Exact Games," Research Memorandum 039, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  2. Yan-An Hwang, 2013. "A note on the core," Journal of Global Optimization, Springer, vol. 55(3), pages 627-632, March.
  3. Nessah, Rabia & Tazdaı¨t, Tarik, 2013. "Absolute optimal solution for a compact and convex game," European Journal of Operational Research, Elsevier, vol. 224(2), pages 353-361.

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