We will introduce the notation of the generalized reduced game to “unify” the representations for maximal subclasses of the classes of essential games (superadditive games and convex games) that are closed under reduction in the sense of Sobolev (1975), Hart and Mas-Colell (1989), and Moulin...

We will introduce the notation of the generalized reduced game to “unify” the representations for maximal subclasses of the classes of essential games (superadditive games and convex games) that are closed under reduction in the sense of Sobolev (1975), Hart and Mas-Colell (1989), and Moulin...

We will find 3 maximal subclasses with respect to essential, superadditive and convex games, respectively such that a game is in one subclass, so are its reduced games.

We prove that the core on the set of all transferable utility games with players contained in a universe of at least five members can be axiomatized by the zero inessential game property, covariance under strategic equivalence, anonymity, boundedness, the weak reduced game property, the converse...