The socially stable core in structured transferable utility games

We consider cooperative games with transferable utility (TU-games), in which we allow for a social structure on any coalition, for instance a network, a hierarchical ordering or a dominance relation. For every coalition the relative strength of a player within that coalition is induced by its social structure and is measured by a power function. We call a payoff vector socially stable if there is a collection of coalitions that can sustain it and at which all players have the same power. A payoff vector is called economically stable if it belongs to the core of the superadditive cover of the game. The socially stable core consists of the socially and economically stable payoff vectors. We show that the socially stable core is non-empty if the game itself is socially stable. The socially stable core consists of a finite number of faces of the set of economically stable payoff vectors. Generically, it consists of a finite number of payoff vectors. Convex TU-games have a non-empty socially stable core, irrespective of the underlying social structure. When the game is permutationally convex, the socially stable core is shown to be non-empty if the power vectors are permutationally consistent and is shown to contain a unique element if the power vectors are permutationally compatible. We demonstrate the usefulness of the concept of the socially stable core by applying it to structured hierarchy games. We also present applications concerning sequencing games and the distribution of water. JEL classification: C60, C70, D70