On the core of a collection of coalitions

J. Derks*, H. Reijnierse

*Corresponding author for this work

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For a collection Omega of subsets of a finite set N we define its core to be equal to the polyhedral cone (x is an element of IRN : Sigma(i is an element of N) x(i) = 0 and Sigma(i is an element of s) x(i) greater than or equal to 0 for all S is an element of Omega). This note describes several applications of this concept in the field of cooperative game theory. Especially collections Omega are considered with core equal to {0}. This property of a one-point core is proved to be equivalent to the non-degeneracy and balancedness of Omega. Further, the notion of exact cover is discussed and used in a second characterization of collections Omega with core equal to {0}.
Original languageEnglish
Pages (from-to)451-459
Number of pages9
JournalInternational Journal of Game Theory
Issue number3
Publication statusPublished - 1998

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