The Average Tree value for Hypergraph Games

Liying Kang, Anna Khmelnitskaya, Erfang Shan, A.J.J. Talman, Guang Zhang

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Abstract

We consider transferable utility cooperative games (TU games) with limited cooperation introduced by 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. We also provide axiomatization of the average tree value for hypergraph games on the subclasses of cycle-free hypergraph games, hypertree games and cycle hypergraph games.
Original languageEnglish
Place of PublicationTilburg
PublisherCentER, Center for Economic Research
Number of pages24
Volume2020-005
Publication statusPublished - 5 Feb 2020

Publication series

NameCentER Discussion Paper
Volume2020-005

Keywords

  • TU game
  • hypergraph communication structure
  • average tree value
  • component fairness

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    Kang, L., Khmelnitskaya, A., Shan, E., Talman, A. J. J., & Zhang, G. (2020). The Average Tree value for Hypergraph Games. (CentER Discussion Paper; Vol. 2020-005). CentER, Center for Economic Research.