### Abstract

Original language | English |
---|---|

Pages (from-to) | 315-333 |

Journal | Journal of Combinatorial Optimization |

Volume | 39 |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 2020 |

### Fingerprint

### Keywords

- TU game
- directed communication structure
- marginal contribution vector
- Myerson value
- average tree solution
- stability

### Cite this

*Journal of Combinatorial Optimization*,

*39*(2), 315-333. https://doi.org/10.1007/s10878-019-00471-5

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*Journal of Combinatorial Optimization*, vol. 39, no. 2, pp. 315-333. https://doi.org/10.1007/s10878-019-00471-5

**The average covering tree value for directed graph games.** / Khmelnitskaya, Anna; Selcuktu, Ozer; Talman, A.J.J.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - The average covering tree value for directed graph games

AU - Khmelnitskaya, Anna

AU - Selcuktu, Ozer

AU - Talman, A.J.J.

PY - 2020/2

Y1 - 2020/2

N2 - 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 it 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.

AB - 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 it 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.

KW - TU game

KW - directed communication structure

KW - marginal contribution vector

KW - Myerson value

KW - average tree solution

KW - stability

U2 - 10.1007/s10878-019-00471-5

DO - 10.1007/s10878-019-00471-5

M3 - Article

VL - 39

SP - 315

EP - 333

JO - Journal of Combinatorial Optimization

JF - Journal of Combinatorial Optimization

SN - 1382-6905

IS - 2

ER -