Owen coalitional value without additivity axiom

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

Shapley value for constant-sum games

It is proved that Young's axiomatization for the Shapley value by marginalism, efficiency, and symmetry is still valid for the Shapley value defined on the class of nonnegative constant-sum games and on the entire class of constant-sum games as well. To support an interest to study the class of nonnegative constant-sum games we show that such a game appears under reasonable reconsideration of the initial TU game before applying one or another solution concept

1-concave basis for TU games

The first stage of research, twenty years ago, on the subclass of 1-convex TU games dealt with its characterization through some regular core structure. Appealing abstract and practical examples of 1-convex games were missing until now. Both drawbacks are solved. On the one hand, a generating set for the cone of 1-concave cost games is introduced with clear affinities to the unanimity games taking into account the complementary transformation on coalitions. The dividends within this new game representation are used to characterize the 1-concavity constraint as well as to investigate the core property of the Shapley value for cost games. We present a simple formula to compute the nucleolus and the τ-value within the class of 1-convex/1-concave games and show that in a 1-convex/1-concave game there is an explicit relation between the nucleolus and the Shapley value. On the other hand, an appealing practical example of 1-concave cost game has cropped up not long ago in Sales’s Ph.D study of Catalan university library consortium for subscription to journals issued by Kluwer publishing house, the so-called library cost game which turn out to be decomposable into the abstract 1-concave cost games of the generating set mentioned above

Semiproportional values for TU games

The goal of the paper is to introduce a family of values for transferable utility cooperative games that are proportional for two-person games and as well satisfying some combinatorial structure composed by contributions of complementary coalitions or, to less extent, marginal contributions by players