The average tree value for hypergraph games

Liying Kang, Anna Khmelnitskaya, Erfang Shan, Dolf Talman*, Guang Zhang

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review


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.
Original languageEnglish
Pages (from-to)437-460
Number of pages24
JournalMathematical Methods of Operations Research
Publication statusPublished - 1 Dec 2021


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


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