### Abstract

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 language | English |
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Pages (from-to) | 451-459 |

Number of pages | 9 |

Journal | International Journal of Game Theory |

Volume | 27 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1998 |

## Cite this

Derks, J., & Reijnierse, H. (1998). On the core of a collection of coalitions.

*International Journal of Game Theory*,*27*(3), 451-459. https://doi.org/10.1007/s001820050084