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Minimal Exact Balancedness

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  • Lohmann, E.R.M.A.
  • Borm, P.E.M.
  • Herings, P.J.J.

    (Tilburg University, Center for Economic Research)

Abstract

To verify whether a transferable utility game is exact, one has to check a linear inequality for each exact balanced collection of coalitions. This paper studies the structure and properties of the class of exact balanced collections. Comparing the definition of exact balanced collections with the definition of balanced collections, the weight vector of a balanced collection must be positive whereas the weight vector for an exact balanced collection may contain one negative weight. We investigate minimal exact balanced collections, and show that only these collections are needed to obtain exactness. The relation between minimality of an exact balanced collection and uniqueness of the corresponding weight vector is analyzed. We show how the class of minimal exact balanced collections can be partitioned into three basic types each of which can be systematically generated.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2011-012.

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Date of creation: 2011
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Handle: RePEc:dgr:kubcen:2011012

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Web page: http://center.uvt.nl

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Keywords: Cooperative games; exact games; exact balanced collections;

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  1. Péter Csóka & P. Jean-Jacques Herings & László Á. Kóczy, 2007. "Balancedness Conditions for Exact Games," Working Paper Series 0805, Óbuda University, Keleti Faculty of Business and Management, revised May 2008.
  2. Csóka, Péter & Herings, P. Jean-Jacques & Kóczy, László Á,, 2007. "Stable Allocations of Risk," Research Memorandum 040, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  3. Hans Haller & Jean Derks, 1999. "Weighted nucleoli," International Journal of Game Theory, Springer, vol. 28(2), pages 173-187.
  4. Calleja, Pedro & Borm, Peter & Hendrickx, Ruud, 2005. "Multi-issue allocation situations," European Journal of Operational Research, Elsevier, vol. 164(3), pages 730-747, August.
  5. 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.
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