Farsighted coalitional stability in TU-games

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...

• Type: Journal
• Year: 2008
• Where: MSS
• Authors: Sylvain Béal, Jacques Durieu, Philippe Solal
• Keywords: Coalitional Stability, Farsighted, Hardware, MSS 2008, Stable