Minimal exact balancedness

E. Lohmann, P. Borm, P.J.J. Herings

Research output: Contribution to journalArticleAcademicpeer-review

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
Pages (from-to)127-135
Number of pages9
JournalMathematical Social Sciences
Volume64
Issue number2
DOIs
Publication statusPublished - Sep 2012

Keywords

  • CHARACTERISTIC FUNCTION GAME
  • NUCLEOLUS
  • CORES
  • SETS

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