The average tree value for hypergraph games

Liying Kang, Anna Borisovna Khmelnitskaya, Erfang Shan, Dolf 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 PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages23
Publication statusPublished - 20 Feb 2020

Publication series

NameTW-Memoranda
PublisherUniversity of Twente, Department of Applied Mathematics
No.2068
ISSN (Print)1874-4850

Keywords

  • TU game
  • Hypergraph communication structure
  • Average tree value
  • Component fairness

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  • Cite this

    Kang, L., Khmelnitskaya, A. B., Shan, E., Talman, D., & Zhang, G. (2020). The average tree value for hypergraph games. (TW-Memoranda; No. 2068). Enschede: University of Twente, Department of Applied Mathematics.