Farsighted coalitional stability in TU-games

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 set. We show that every TU-game has a nonempty largest consistent set. Moreover, the proof of this result points out 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 is equal to the set of imputations of the game. Next, the relationships between the core and the largest consistent set are studied in superadditive TU-games and in clan games. In the last section, we explore the stability of the Shapley value. It is proved that the Shapley value of a superadditive TU-game is always a stable imputation: it is a core imputation or it constitutes a farsighted stable set. A necessary and sufficient condition for a superadditive TU-game to have the Shapley value in the largest consistent set is given.