Farsighted Coalitional Stability in TU-games

Sylvain Béal (1) , Jacques Durieu (1) , Philippe Solal (1)

1 CREUSET - Centre de Recherche Economique de l'Université de Saint-Etienne

We study farsighted coalitional stability in the context of TU-games. We show that every TU-game has a nonempty largest consistent set and that each TU-game has a von Neumann–Morgenstern farsighted stable set. We characterize the collection of von Neumann–Morgenstern farsighted stable sets. We also show that the farsighted core is either empty or equal to the set of imputations of the game. In the last section, we explore the stability of the Shapley value. The Shapley value of a superadditive game is a stable imputation: it is a core imputation or it constitutes a von Neumann–Morgenstern farsighted stable set. A necessary and sufficient condition for a superadditive game to have the Shapley value in the largest consistent set is given

Keywords: Cooperative games; Farsighted core; Consistent set; von Neumann–Morgenstern farsighted stable set; Shapley value Cooperative games; Shapley value

Domains: Economics and Finance

Sylvain Béal, Jacques Durieu, Philippe Solal. Farsighted Coalitional Stability in TU-games. Mathematical Social Sciences, 2008, 56 (3), pp.303-313. ⟨10.1016/j.mathsocsci.2008.06.003⟩. ⟨hal-00334049⟩