### Abstract

We introduce a single-valued solution concept, the so-called average covering tree value, for the class of transferable utility games with limited communication structure represented by a directed graph. The solution is the average of the marginal contribution vectors corresponding to all covering trees of the directed graph. The covering trees of a directed graph are those (rooted) trees on the set of players that preserve the dominance relations between the players prescribed by the directed graph. The average covering tree value is component efficient and under a particular convexity-type condition is stable. For transferable utility games with complete communication structure the average covering tree value equals to the Shapley value of the game. If the graph is the directed analog of an undirected graph the average covering tree value coincides with the gravity center solution.

Original language | Undefined |
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Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 18 |

Publication status | Published - May 2012 |

### Publication series

Name | Memorandum / Department of Applied Mathematics |
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Publisher | University of Twente, Department of Applied Mathematics |

No. | 1981 |

ISSN (Print) | 1874-4850 |

ISSN (Electronic) | 1874-4850 |

### Keywords

- IR-80404
- METIS-289643
- JEL-C71
- EWI-21864
- TU game
- Stability
- Myerson value
- Directed communication structure
- Marginal contribution vector
- Average tree solution

## Cite this

Khmelnitskaya, A. B., Selcuk, Ö., & Talman, D. (2012).

*The average covering tree value for directed graph games*. (Memorandum / Department of Applied Mathematics; No. 1981). Enschede: University of Twente, Department of Applied Mathematics.