### Abstract

A vector of balanced weights infers an inequality that games with a nonempty core obey.This paper gives a generalization of the notion `vector of balanced weights'.Herewith it provides necessary and sufficient conditions to determine whether a TU-game has a population monotonic allocation scheme or not. Furthermore it shows that every 4-person integer valued game with a population monotonic allocation scheme has an integer valued population monotonic allocation scheme and it gives an example of a 7-person integer valued game that has only non-integer valued population monotonic allocation schemes.

Original language | English |
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Place of Publication | Tilburg |

Publisher | Microeconomics |

Number of pages | 14 |

Volume | 2000-99 |

Publication status | Published - 2000 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 2000-99 |

### Keywords

- game theory

## Cite this

Norde, H. W., & Reijnierse, J. H. (2000).

*A Dual Description of the Class of Games with a Population Monotonic Allocation Scheme*. (CentER Discussion Paper; Vol. 2000-99). Microeconomics.