The average tree value for hypergraph games
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 as...
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| Veröffentlicht in: | Mathematical methods of operations research (Heidelberg, Germany) Germany), 2021-12, Vol.94 (3), p.437-460 |
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| container_title | Mathematical methods of operations research (Heidelberg, Germany) |
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| creator | Kang, Liying Khmelnitskaya, Anna Shan, Erfang Talman, Dolf Zhang, Guang |
| description | 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. |
| doi_str_mv | 10.1007/s00186-021-00762-w |
| format | Article |
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| 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 |
| title | The average tree value for hypergraph games |
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