Years and Authors of Summarized Original Work
2006; Deng, Fang, Sun
Problem Definition
Cooperative game theory considers how to distribute the total income generated by a set of participants in a joint project to individuals. The Nucleolus, trying to capture the intuition of minimizing dissatisfaction of players, is one of the most well-known solution concepts among various attempts to obtain a unique solution. In Deng, Fang, and Sun’s work [3], they study the Nucleolus of flow games from the algorithmic point of view. It is shown that, for a flow game defined on a simple network (arc capacity being all equal), computing the Nucleolus can be done in polynomial time, and for flow games in general cases, both the computation and the recognition of the Nucleolus are \(\mathcal{N}\mathcal{P}\)-hard.
A cooperative (profit) game (N, v) consists of a player set N = {1, 2, ⋯ , n} and a characteristic function v : 2N → R with v(∅) = 0, where the value v(S)(S ⊆ N) is interpreted as the profit...
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Fang, Q. (2016). Nucleolus. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_260
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