The core and the Shapley value seem to be the most widely discussed and applied solution concepts in cooperative game theory. Of the several other concepts, this book will discuss only the nucleolus. Like the Shapley value, the nucleolus is never null and assigns a unique net payoff to every agent in the game. The nucleolus has the further property that if the core is not null, the nucleolus is an element of it. Thus, the nucleolus can be thought of as a core assignment algorithm; that is, as a basis for singling out a particular imputation in the core when the core is not unique. The nucleolus can be computed by linear programming, although there are some complications, even for a game as simple as this one. The nucleolus has some desirable properties. Like the Shapley value and the core, it is covariant over strategic equivalence and has an equal treatment property. Like the core, the nucleolus is anonymous. It is not additive and lacks the null player property.8 For more detail on the nucleolus and an extension that will be applied in Part II, see McCain (2013, Chapters 1, 6).

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