TU game, Cooperation structure, Myerson value, Component efficiency, Deletion link property, Harsanyi dividends, Sharing a river,

Abstract. We show that the Owen value for TU games with coalition structure can be characterized without additivity axiom similarly as it was done by Young for the Shapley value for general TU games. Our axiomatization via four axioms of efficiency, marginality, symmetry across coalitions, and symmetry within coalitions is obtained from the original Owen's one by replacement of the additivity and null-player axioms via marginality. We show that the alike axiomatization for the generalization of the Owen value suggested by Winter for games with level structure is valid as well.

The study of 1-convex/1-concave TU games possessing a nonempty core and for which the nucleolus is linear was initiated by Driessen and Tijs (Methods Oper. Res. 46:395-406, 1983) and Driessen (OR Spectrum 7:19-26, 1985). However, until recently appealing abstract and practical examples of these classes of games were missing. The paper solves these drawbacks. We introduce a 1-concave basis for the entire space of all TU games wherefrom it follows that every TU game is either 1-convex/1-concave or is a sum of 1-convex and 1-concave games. Thus we may conclude that the classes of 1-convex/1-concave games constitute rather considerable subsets in the entire game space. On the other hand, an appealing practical example of 1-concave game has cropped up in Sales's study (Ph. D. thesis, 2002) of Catalan university library consortium for subscription to journals issued by Kluwer publishing house. The so-called library game turns out to be decomposable into suitably chosen 1-concave games of the basis mentioned above.

We consider transferable utility cooperative games (TU games) with limited cooperation introduced by 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. We also provide axiomatization of the average tree value for hypergraph games on the subclasses of cycle-free hypergraph games, hypertree games and cycle hypergraph games.