The Nucleolus

Hans Peters

Chapter 19 in Game Theory, 2015, pp 343-359 from Springer

Abstract: Abstract The core of a game with transferable utility can be a large set, but it can also be empty. The Shapley value assigns to each game a unique point, which, however, does not have to be in the core. The nucleolus assigns to each game with a nonempty imputation set a unique element of that imputation set; moreover, this element is in the core if the core of the game is nonempty. The pre-nucleolus exists for every essential game (and does not have to be an imputation, even if the imputation set is nonempty), but for balanced games it coincides with the nucleolus.

Keywords: Linear Order; Lexicographic Order; Grand Coalition; Payoff Vector; Balance Game (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-662-46950-7_19

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