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Abstract. We study farsighted coalitional stability in the context of TUgames. Chwe (1994, p.318) notes that, in this context, it is difficult to prove nonemptiness of the largest consistent. We show that every TU-game has a nonempty largest consistent set. Moreover, the proof of this result allows to conclude that each TU-game has a farsighted stable set. We go further by providing a characterization of the collection of farsighted stable sets in TU-games. We also show that the farsighted core of a TU-game is empty or equal to the set of imputations of the game. Next, we study the relationships between the core and the largest consistent set in superadditive TU-games and in clan games. In the last section, we explore the stability of the Shapley value in superadditive TU-games. We show that the Shapley value is always a stable imputation. More precisely, if the Shapley value does not belong to the core, then it constitutes a farsighted stable set. We provide a necessary and sufficient condition for a superadditive TU-game to have the Shapley value in the largest consistent set.

We introduce new axioms for the class of all TU-games with a fixed but arbitrary player set, which require either invariance of an allocation rule or invariance of the payoff assigned by an allocation rule to a specified subset of players in two related TU-games. Comparisons with other axioms are provided. These new axioms are used to characterize the Shapley value, the equal division rule, the equal surplus division rule and the Banzhaf value. The classical axioms of efficiency, anonymity, symmetry and additivity are not used.

We consider communication situations games being the combination of a TU-game and a communication graph. We study the average tree (AT) solutions introduced by Herings et al. [9] and [10]. The AT solutions are defined with respect to a set, say T , of rooted spanning trees of the communication graph. We characterize these solutions by efficiency, linearity and an axiom of T -hierarchy. Then we prove the following results. Firstly, the AT solution with respect to T is a Harsanyi solution if and only if T is a subset of the set of trees introduced in [10]. Secondly, the latter set is constructed by the classical DFS algorithm and the associated AT solution coincides with the Shapley value when the communication graph is complete. Thirdly, the AT solution with respect to trees constructed by the other classical algorithm BFS yields the equal surplus division when the communication graph is complete.

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