### Abstract

In this paper we generalise marginal vectors and permutational convexity.We show that if a game is generalised permutationally convex, then the corresponding generalised marginal vector is a core element.Furthermore we refine the concept of permutational convexity and show that this refinement yields a sufficient condition for the corresponding marginal vector to be a core element.Finally, we prove that permutational convexity is equivalent to a restricted set of inequalities and that if a game is permutationally convex with respect to an order, then it is permutationally convex with respect to a related order as well.

Original language | English |
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Place of Publication | Tilburg |

Publisher | Operations research |

Number of pages | 18 |

Volume | 2005-83 |

Publication status | Published - 2005 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 2005-83 |

### Keywords

- Cooperative game theory
- marginal vectors
- permutational convexity

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## Cite this

van Velzen, S., Hamers, H. J. M., & Norde, H. W. (2005).

*A Note on Permutationally Convex Games*. (CentER Discussion Paper; Vol. 2005-83). Operations research.