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The transferable utility games with limited cooperation can be represented by a hypergraph communication structure, called hypergraph games. Such a structure consists of a collection of coalitions, the hyperlinks of the hypergraph, for which it is assumed that only the coalitions that are hyperlinks or the connected union of hyperlinks are able to cooperate and obtain their worth. On the class of hypergraph games we introduce the average tree solution, being for each component of the hypergraph the average of a specific collection of marginal contribution vectors. On the class of cycle-free hypergraph games, the average tree solution is characterized by component efficiency and component fairness. The latter property states that when removing a hyperlink the average payoff difference is the same for every resulting component. While removing a link between two nodes in a cycle-free graph results in two components, this number can be more than two when a hyperlink in a cycle-free hypergraph is removed.
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