摘要
本文旨在研究有限合作賽局的勢。在第一節中,我們回顧一些有限合作賽局的基本概念,諸如:承 載子,冗員,Shapley值以及排列賽局,另外我們也回顧向量空間集合X對應到體F的函數集及N的冪集合對應到體F的函數集中的一些基底。在第二節中, 我們介紹在N的冪集合上的複函數的勢,並且研究在n人有限合作賽局所成的集合上的勢函數P的基本性質。在第三節中,我們介紹定義在複函數的梯度並證明一個賽局的勢的梯度即為該賽局的Shapley值。
關鍵字
賽局的勢並列摘要
The purpose of this thesis is to study the notion of the potential of an n-person cooperative game. In section 1, we review some basic notions about finite cooperative games such as carriers,dummies, Shapley values and permuted games, some bases of the vector spaces which are the sets of all functions from X into F and the sets of all functions from the power set of N into F are also introduced. In section 2, we introduce the potential of a complex function on the power set of N and study some elementary properties of the potential map P on the set of all n-person cooperative games. In section 3, we introduce the (discrete) gradient of a complex function on the power set of N and show that the gradient of the potential of a game is the Shapley value of the game.