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The nucleolus is a unique solution concept for a cooperative game. It belongs to the kernel of the game. Given m games over disjoint sets of players and an m-player game, one defines a compound game over the union of the m disjoint sets. These m games are the components and the above m-player game is called the quotient.The nucleolus of the compound game is a combination of the nucleoluses of the components, i.e., the payoffs in the components are proportional to the payoffs in the compound. The combination depends on the quotient game and on the two highest levels of excesses with respect to the nucleoluses of the components. This combination is the solution of a problem of the same nature as that of the nucleolus.

Nucleoluses of Compound Simple Games