The average tree value for hypergraph games

Liying Kang (), Anna Khmelnitskaya (), Erfang Shan (), Adolphus Talman and Guang Zhang ()
Additional contact information
Liying Kang: Shanghai University
Anna Khmelnitskaya: Saint-Petersburg State University
Erfang Shan: Shanghai University
Guang Zhang: University of Shanghai for Science and Technology

Mathematical Methods of Operations Research, 2021, vol. 94, issue 3, No 4, 437-460

Abstract: 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’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: TU game; Hypergraph communication structure; Average tree value; Component fairness; 91A12; 91A43 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (4)

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Working Paper: The Average Tree value for Hypergraph Games (2020)
Working Paper: The Average Tree value for Hypergraph Games (2020)
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DOI: 10.1007/s00186-021-00762-w

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