The average tree value for hypergraph games

• Published in: Mathematical methods of operations research (Heidelberg, Germany) Germany), 2021-12, Vol.94 (3), p.437-460
• Main Authors: Kang, Liying, Khmelnitskaya, Anna, Shan, Erfang, Talman, Dolf, Zhang, Guang
• Format: Article
• Language: English
• Subjects: Autumn; Business and Management; Calculus of Variations and Optimal Control; Optimization; Cooperation; Game theory; Games; Graph theory; Graphs; Mathematics; Mathematics and Statistics; Operations research; Operations Research/Decision Theory; Original Article
• ISSN: 1432-2994; 1432-5217
• DOI: 10.1007/s00186-021-00762-w

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.