I would like to understand in the snippet below in the definition $2.1$, what does it mean for a game $(N,v)$ to have a nucleolus. And also what does $IG$ stand for.
2026-04-22 10:45:52.1776854752
nucleolus of a game
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1
A game has a nucleolus whenever it is essential (Def.2.1), that is to say that the game has a non-empty imputation set. If it is inessential (reverse of Def. 2.1), then the imputation set is empty, and the nucleolus does not exist, since it is a point in the imputation set that satisfies accentuated geometric properties (cf. Maschler,Peleg and Shapley (1979), Geometric Properties of the Kernel, Nucleolus and Related Solution Concepts, Mathematics of Operations Research, pp.303-338).