Part III consists of three chapters, each extending the basic model of non-cooperative coalition formation in Part II in three directions: renegotiations, participation, and incomplete information. Chapter 8 presents a coalitional bargaining model with renegotiations and explores whether and how renegotiations can enhance the efficiency of coalition formation. Chapter 9 considers a new participation rule called an open access rule, under which players are free to participate in coalitions without invitations from proposers. Participation needs the approval of incumbent members of coalitions. The new model is motivated for the study of international environmental negotiations. Chapter 10 presents the core theory of n-person cooperative games with incomplete information. Coalition formation becomes a complicated process when players have private information. The incomplete informational core considers endogenous information leakage during negotiations. We extend a non-cooperative bargaining model in Chapter 5 to the case of incomplete information.