平衡賽局之研究

本論文的目的是在以稍微帶有幾何方法的方式學習平衡合作賽局的概念，某些已知的觀念和結果將用一系列的例子來闡述。我們將足標為整數或集合的有限實數族或的當成歐幾里得空間的點並給一些非空有界閉集合例子。　　一個特殊多面體子集的端點的確切解的計算對平衡匯集和最小平衡匯集概念的了解是有幫助的。線性規劃，尤其有關非對稱型式的對偶知識必需具備，而且我們將透過一些例子來說明這些觀念。一個給定賽局的核的非空性是跟一個與該賽局對應的可行線性規劃的值有關，而且我們可以藉由該線性規劃的對偶規劃來處理這方面的問題得到平衡賽局的概念。

關鍵字

平衡賽局；核；非對稱型式的對偶

並列摘要

The purpose of this thesis is to learn the concept of balanced cooperative game in a somewhat geometrical approach. Some well known notions and results are explained by a series of examples. We consider the finite real families or indexed by integers or sets as points in suitable Euclidean spaces and give some examples of nonempty closed bounded sets. The exact solution of the extreme points of a special polyhedral subset is computed which is helpful to realize the notions of balanced collections and minimal balanced collections. Linear programming, especially the asymmetric form of duality, is needed, and we choose some examples to illustrate these notions. The nonemptyness of the core of a given game is closed related to the value of a corresponding feasible linear program and we may handle this by studying its dual problem which would lead us to get a concept of balanced game.