of players. The social structure is utilized to refine the core of the game. For every coalition the relative strength of … stable core is the set of socially stable elements of the core. We show that the socially stable core is non-empty if the … game itself is socially stable. In general the socially stable core consists of a finite number of faces of the core and …

structure is utilized to refine the core of the game. For every coalition the relative strength of a player within that … the collection of coalitions that can attain it, all players have the same power. The socially stable core is the set of … socially stable elements of the core. We show that the socially stable core is non-empty if the game itself is socially stable …

The purpose of this paper is to prove the equal treatment property for the $\star$-core allocations of an atomless … economy without any condition on the data of economy. This result prompts the same property for the core allocations. …