In this note we show that on the domain of fuzzy NTU games whose core is non-empty, the core is the only solution satisfying non-emptiness, individual rationality and the reduced game property.

In the presence of independence of undominating alternatives and continuity, we show that the symmetric egalitarian solution is the unique symmetric solution satisfying marginal monotonicity.

In bankruptcy problems we characterize the random arrival rule by means of CG-consistency and population monotonicity.

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...