The average tree value for hypergraph games

Standard

The average tree value for hypergraph games. / Kang, Liying; Khmelnitskaya, Anna; Shan, Erfang; Talman, Dolf; Zhang, Guang.

In: Mathematical Methods of Operations Research, Vol. 94, No. 3, 12.2021, p. 437-460.

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

Harvard

Kang, L, Khmelnitskaya, A, Shan, E, Talman, D & Zhang, G 2021, 'The average tree value for hypergraph games', Mathematical Methods of Operations Research, vol. 94, no. 3, pp. 437-460. https://doi.org/10.1007/s00186-021-00762-w

APA

Kang, L., Khmelnitskaya, A., Shan, E., Talman, D., & Zhang, G. (2021). The average tree value for hypergraph games. Mathematical Methods of Operations Research, 94(3), 437-460. https://doi.org/10.1007/s00186-021-00762-w

Vancouver

Kang L, Khmelnitskaya A, Shan E, Talman D, Zhang G. The average tree value for hypergraph games. Mathematical Methods of Operations Research. 2021 Dec;94(3):437-460. https://doi.org/10.1007/s00186-021-00762-w

Author

Kang, Liying ; Khmelnitskaya, Anna ; Shan, Erfang ; Talman, Dolf ; Zhang, Guang. / The average tree value for hypergraph games. In: Mathematical Methods of Operations Research. 2021 ; Vol. 94, No. 3. pp. 437-460.

BibTeX

@article{cf7edd26acb24e6db2a02f516bbc8a32,

title = "The average tree value for hypergraph games",

abstract = "We consider transferable utility cooperative games (TU games) with limited cooperation introduced by a hypergraph communication structure, the so-called hypergraph games. A hypergraph communication structure is given by a collection of coalitions, the hyperlinks of the hypergraph, for which it is assumed that only coalitions that are hyperlinks or connected unions of hyperlinks are able to cooperate and realize their worth. We introduce the average tree value for hypergraph games, which assigns to each player the average of the player{\textquoteright}s marginal contributions with respect to a particular collection of rooted spanning trees of the hypergraph, and study its properties. We show that the average tree value is stable on the subclass of superadditive cycle-free hypergraph games. We also provide axiomatizations of the average tree value on the subclasses of cycle-free hypergraph games, hypertree games, and cycle hypergraph games.",

keywords = "Average tree value, Component fairness, Hypergraph communication structure, TU game",

author = "Liying Kang and Anna Khmelnitskaya and Erfang Shan and Dolf Talman and Guang Zhang",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2021",

month = dec,

doi = "10.1007/s00186-021-00762-w",

language = "English",

volume = "94",

pages = "437--460",

journal = "Mathematical Methods of Operations Research",

issn = "1432-2994",

publisher = "Physica-Verlag",

number = "3",

}

RIS

TY - JOUR

T1 - The average tree value for hypergraph games

AU - Kang, Liying

AU - Khmelnitskaya, Anna

AU - Shan, Erfang

AU - Talman, Dolf

AU - Zhang, Guang

PY - 2021/12

Y1 - 2021/12

N2 - We consider transferable utility cooperative games (TU games) with limited cooperation introduced by a hypergraph communication structure, the so-called hypergraph games. A hypergraph communication structure is given by a collection of coalitions, the hyperlinks of the hypergraph, for which it is assumed that only coalitions that are hyperlinks or connected unions of hyperlinks are able to cooperate and realize their worth. We introduce the average tree value for hypergraph games, which assigns to each player the average of the player’s marginal contributions with respect to a particular collection of rooted spanning trees of the hypergraph, and study its properties. We show that the average tree value is stable on the subclass of superadditive cycle-free hypergraph games. We also provide axiomatizations of the average tree value on the subclasses of cycle-free hypergraph games, hypertree games, and cycle hypergraph games.

AB - We consider transferable utility cooperative games (TU games) with limited cooperation introduced by a hypergraph communication structure, the so-called hypergraph games. A hypergraph communication structure is given by a collection of coalitions, the hyperlinks of the hypergraph, for which it is assumed that only coalitions that are hyperlinks or connected unions of hyperlinks are able to cooperate and realize their worth. We introduce the average tree value for hypergraph games, which assigns to each player the average of the player’s marginal contributions with respect to a particular collection of rooted spanning trees of the hypergraph, and study its properties. We show that the average tree value is stable on the subclass of superadditive cycle-free hypergraph games. We also provide axiomatizations of the average tree value on the subclasses of cycle-free hypergraph games, hypertree games, and cycle hypergraph games.

KW - Average tree value

KW - Component fairness

KW - Hypergraph communication structure

KW - TU game

UR - http://www.scopus.com/inward/record.url?scp=85120381106&partnerID=8YFLogxK

U2 - 10.1007/s00186-021-00762-w

DO - 10.1007/s00186-021-00762-w

M3 - Article

VL - 94

SP - 437

EP - 460

JO - Mathematical Methods of Operations Research

JF - Mathematical Methods of Operations Research

SN - 1432-2994

IS - 3

ER -

ID: 52851171