臺灣博碩士論文加值系統

這篇論文的研究主題可分為兩個部分，分別與合作對局論中的兩個重要的解nucleolus以及Shapley value有關。
我們的第一個主題是關於nucleolus的線性區域(linearity region)。由於nucleolus是一個單值(single-valued)的解，因此我們可以將之視為一個定義在對局空間(game space)上的函數。而在這裡所謂的線性區域(linearity region)指的是對局空間中的一個集合使得在此集合上nucleolus是一個線性函數。Kohlberg 在1971年介紹了balanced array的概念，並且使用這個概念來刻劃nucleolus的線性區域。在第二章中，我們定義了balanced topology的概念用以推廣balanced array，並且使用balanced topology的語言來刻劃nucleolus的最大線性區域(maximal linearity region)。然而，我們同時也發現並不是所有的線性區域都可以使用balanced topology加以刻劃。因此，找出所有的最大線性區域仍然是一個有意思的研究方向。在2.6節中，我們給了一個例子來說明這件事。
我們的第二個主題是推廣Shapley value到具有外部性的合作對局上(games with partition function form)。Thrall和Lucas在1963年定義了具有外部性的合作對局用以推廣TU games。所謂具有外部性的合作對局指的是當一個團體合作時，他們合作所帶來的利益與其外部成員的結盟情形有關。Shapley vlaue的想法與邊際貢獻(marginal contribution)的概念有著相當密切的關係。因此，我們的基本想法是希望能將邊際貢獻的概念推廣到具有外部性的合作對局上。在第三章中，我們提出一種在具外部性的合作賽局中評估邊際貢獻的辦法，我們稱之為coalitionally extracted marginal contribution(CEMC)。根據CEMC的想法，我們提出了一個在具外部性的合作賽局上的解，並且我們證明了在不具外部性的合作對局(TU games)上，這個解和原本的Shapley value是一樣的。此外，我們也提供了三組公設系統來刻劃這一個解。

CHAPTER 1. INTRODUCTION . . . . . . . . . . . . . . . 1
1.1 The nucleolus and the Shapley value . . . . . . . 1
1.2 De…nitions and conventions .. . . . . . . . . . . 2
1.3 Summary . . . . . . . . . . . . . . . . . . . . . 7
CHAPTER 2. ON THE LINEARITY REGIONS OF THE NUCLEOLUS 9
2.1 Introduction .. . . . . . . . . . . . . . . . . . 9
2.2 Valid array . . . . . . . . . . . . . . . . . . . 10
2.3 Balanced topology . . . . . . . . . . . . . . . . 14
2.4 Maximal linearity region. . . . . . . . . . . . . 24
2.5 Decomposition of \Phi(T ;B_0) . . . . . . . . . . 32
2.6 Two examples . . . . . . . . . . . . . . . . . . 37
CHAPTER 3. CHARACTERIZATIONS OF A VALUE FOR PARTITION FUNC-
TION FORM GAMES . . . . . . . . . . . . . . . . . . . 41
3.1 Introduction . . . . . . . . . . . . . . . . . . 41
3.2 Definitions and facts . . . . . . . . . . . . . . 43
3.3 A value for partition function form games . . . . 45
3.4 Balanced contributions property . . . . . . . . . 53
3.5 Independence. . . . . . . . . . . . . . . . . . . 56
CHAPTER 4. EXTENSIONS . . . . . . . . . . . . . . . . 59
4.1 Several directions. . . . . . . . . . . . . . . . 59
4.2 Appendix. . . . . . . . . . . . . . . . . . . . . 61
REFERENCES CITED. . . . . . . . . . . . . . . . . . . 64

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