Minimal exact balancedness
AbstractTo verify whether a transferable utility game is exact, one has to check a linear inequalityfor each exact balanced collection of coalitions. This paper studies the structure andproperties of the class of exact balanced collections. Comparing the definition of exactbalanced collections with the definition of balanced collections, the weight vector of abalanced collection must be positive whereas the weight vector for an exact balancedcollection 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 InfoPaper provided by Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization in its series Research Memoranda with number 009.
Date of creation: 2011
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operations research and management science;
Other versions of this item:
- Lohmann, E.R.M.A. & Borm, P.E.M. & Herings, P.J.J., 2011. "Minimal Exact Balancedness," Discussion Paper 2011-012, Tilburg University, Center for Economic Research.
- 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).
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
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