The kernel of a cooperative game

Abstract The kernel of a cooperative n‐person game is defined. It is a subset of the bargaining set 𝔐 (i) . Its existence and some of its properties are studied. We apply it to the 3‐person games, to the 4‐person constant‐sum games, to the symmetric and n‐quota games and to games in which only the n and the (n‐1)‐person coalitions are allowed to be non‐flat. In order to illustrate its merits and demerits as a predictor of an actual outcome in a real‐life situation, we exhibit an example in which the kernel prediction seems frustrating. The opinions of other authors are quoted in order to throw some light on this interesting example.