Minimal Exact Balancedness

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

Research output: Working paperDiscussion paperOther research output

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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.
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Volume2011-012
Publication statusPublished - 2011

Publication series

NameCentER Discussion Paper
Volume2011-012

Fingerprint

Balancedness
Exactness
Minimality
Coalitions
Linear Inequalities
Uniqueness
Game
Verify

Keywords

  • Cooperative games
  • exact games
  • exact balanced collections

Cite this

Lohmann, E. R. M. A., Borm, P. E. M., & Herings, P. J. J. (2011). Minimal Exact Balancedness. (CentER Discussion Paper; Vol. 2011-012). Tilburg: Operations research.
Lohmann, E.R.M.A. ; Borm, P.E.M. ; Herings, P.J.J. / Minimal Exact Balancedness. Tilburg : Operations research, 2011. (CentER Discussion Paper).
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Lohmann, ERMA, Borm, PEM & Herings, PJJ 2011 'Minimal Exact Balancedness' CentER Discussion Paper, vol. 2011-012, Operations research, Tilburg.

Minimal Exact Balancedness. / Lohmann, E.R.M.A.; Borm, P.E.M.; Herings, P.J.J.

Tilburg : Operations research, 2011. (CentER Discussion Paper; Vol. 2011-012).

Research output: Working paperDiscussion paperOther research output

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Lohmann ERMA, Borm PEM, Herings PJJ. Minimal Exact Balancedness. Tilburg: Operations research. 2011. (CentER Discussion Paper).