A Hierarchical Model for Cooperative Games
A Hierarchical Model for Cooperative Games
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DOI：
10.1007/978-3-540-79309-0_21
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发表时间：
2008-04
期刊：
影响因子：
--
通讯作者：
U. Faigle;Britta Peis
中科院分区：
文献类型：
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作者：
U. Faigle;Britta Peis
传统上，合作博弈由一个正规化的实值函数给出，该函数是参与者集合N的所有子集的集合。沙普利观察到，如果是一个非负凸（也称为非空），那么游戏的核心是非空的。超模）集合函数。特别地，Shapley值是凸对策的核心成员。我们推广了经典的博弈模型，使得不是N的所有子集都需要形成可行的联盟。我们介绍了一个模型，排名个别球员产生自然的概念，韦伯集和Shapley值在一个非常普遍的情况下。在此框架下，我们建立了单调凸对策核的非空性的Shapley定理。证明如下的贪婪算法，特别是，推广埃德蒙兹的polymatroid贪婪算法。
Classically, a cooperative game is given by a normalized real-valued functionvon the collection of all subsets of the setNof players. Shapley has observed that the core of the game is non-empty ifvis a non-negative convex (a.k.a. supermodular) set function. In particular, the Shapley value of a convex game is a member of the core. We generalize the classical model of games such that not all subsets ofNneed to form feasible coalitions. We introduce a model for ranking individual players which yields natural notions of Weber sets and Shapley values in a very general context. We establish Shapley’s theorem on the nonemptyness of the core of monotone convex games in this framework. The proof follows from a greedy algorithm that, in particular, generalizes Edmonds’ polymatroid greedy algorithm.