Abstract
This thesis deals with some new results of fixed point theory and their applications on game theory. In chapter 2, it is devoted to supply some preliminary geometric facts and the notations used. In particular, a very interesting collection of coalitions ``nonbalanced group'' is proposed. In chapter 3, we introduce a new labelling map which is called -labelling map and several classic well-known covering and labelling theorems, for instance, several variants of KKM theorem, KKMS theorem, Sperner's lemma and Shapley-Sperner's lemma are included. We discuss the relationships among these classic facts and -labelling map. Moreover, we obtained some new covering and labelling results in this chapter. In chapter 4, the existence problems of four different versions of bargaining sets on NTU games which are based on different relationships on the coalitions of objection and counterobjection are studied by results obtained in Chapter 3. In chapter 5, we present two examples to give negative answers of two questions about the nucleolus raised by Kalai. We modify Kalai's excess function such that the nucleolus obtained by it is continuous. Moreover, we employ the Brouwer fixed point theorem to obtain that the nucleolus has interesting relationship with coalition orderings as it does on TU games. In fact, this is the third question of Kalai.