### Abstract

solution the average of the marginal vectors that correspond to the set of rooted trees that are compatible with the quasi-building system. Properties of this solution, called the AMV-value, are studied. Relations with other solutions in the literature are also studied. To establish that the AMV-value is an element of the core, we introduce appropriate convexity-type conditions for the game with respect to the underlying quasi-building system. In case of universal cooperation, the AMV-value coincides with the Shapley value.

Language | English |
---|---|

Article number | 218 |

Pages | 1-13 |

Journal | Discrete Applied Mathematics |

Volume | 218 |

DOIs | |

State | Published - Feb 2017 |

### Fingerprint

### Keywords

- set system
- rooted tree
- core
- convexity
- marginal vector
- Shapley value

### Cite this

*Discrete Applied Mathematics*,

*218*, 1-13. [218]. DOI: 10.1016/j.dam.2016.09.003

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*Discrete Applied Mathematics*, vol. 218, 218, pp. 1-13. DOI: 10.1016/j.dam.2016.09.003

**Cooperative games with restricted formation of coalitions.** / Koshevoy, Gleb; Suzuki, Takamasa; Talman, Dolf.

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

TY - JOUR

T1 - Cooperative games with restricted formation of coalitions

AU - Koshevoy,Gleb

AU - Suzuki,Takamasa

AU - Talman,Dolf

PY - 2017/2

Y1 - 2017/2

N2 - In the study of cooperative games, restricted cooperation between players is typically modeled by a set system of feasible coalitions of the players. In this paper, we go one step further and allow for a distinction among players within a feasible coalition, between those who are able to form the coalition and those who are not. This defines a contracting map, a choice function. We introduce the notion of quasi-building system and require that such a choice function gives rise to a quasi-building system. Many known set systems and structures studied in the literature are covered by quasi-building systems. For transferable utility games having a quasi-building system as cooperation structure we take as asolution the average of the marginal vectors that correspond to the set of rooted trees that are compatible with the quasi-building system. Properties of this solution, called the AMV-value, are studied. Relations with other solutions in the literature are also studied. To establish that the AMV-value is an element of the core, we introduce appropriate convexity-type conditions for the game with respect to the underlying quasi-building system. In case of universal cooperation, the AMV-value coincides with the Shapley value.

AB - In the study of cooperative games, restricted cooperation between players is typically modeled by a set system of feasible coalitions of the players. In this paper, we go one step further and allow for a distinction among players within a feasible coalition, between those who are able to form the coalition and those who are not. This defines a contracting map, a choice function. We introduce the notion of quasi-building system and require that such a choice function gives rise to a quasi-building system. Many known set systems and structures studied in the literature are covered by quasi-building systems. For transferable utility games having a quasi-building system as cooperation structure we take as asolution the average of the marginal vectors that correspond to the set of rooted trees that are compatible with the quasi-building system. Properties of this solution, called the AMV-value, are studied. Relations with other solutions in the literature are also studied. To establish that the AMV-value is an element of the core, we introduce appropriate convexity-type conditions for the game with respect to the underlying quasi-building system. In case of universal cooperation, the AMV-value coincides with the Shapley value.

KW - set system

KW - rooted tree

KW - core

KW - convexity

KW - marginal vector

KW - Shapley value

U2 - 10.1016/j.dam.2016.09.003

DO - 10.1016/j.dam.2016.09.003

M3 - Article

VL - 218

SP - 1

EP - 13

JO - Discrete Applied Mathematics

T2 - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

M1 - 218

ER -