The kernel of a cooperative game

TLDR

The kernel is a subset of the bargaining set 𝔐 (i) and the authors reference other scholars to illuminate an example. The paper defines the kernel of a cooperative n‑person game, studies its existence and properties, and illustrates its predictive merits and demerits with a real‑life example. The authors apply the kernel to 3‑person games, 4‑person constant‑sum games, symmetric and n‑quota games, and games where only n and (n‑1)‑person coalitions are non‑flat. The example shows that the kernel prediction can be frustrating, highlighting its limitations as a predictor of actual outcomes.

Abstract

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.