Values for cooperative games with restricted coalition formation

Abstract

In the standard cooperative games, it is often implicitly assumed that any coalition may form and the worth of the grand coalition will be divided among all players. However, since the coalition formation problems may depend on many factors (for example, the sharing rule used), it is not unlikely that in certain cases the players prefer other options to organize themselves. This thesis focuses on values for games with restricted coalition formation and can be divided into two parts according to the factors that influence the coalition formation. The first part consists of Chapters 2 and 3, where the coalition formation is affected by the characteristic functions or a given solution concept of games. Chapter 2 allows any two players to exchange their positions, and thereby claims that not all ordered coalitions can be formed. Chapter 3 studies a combination of coalition formation and stability for cooperative games, where a set of players has incentive to split from the original game if that is beneficial to them. The second part consists of Chapters 4-7, which pay attention to the cooperative situations where the coalition formation is restricted by the given social, economic and other structures. Chapter 4 defines and implements a multi-step Shapley value for cooperative games with levels structures. Chapter 5 analyzes the weighted hypergraph communication situations and argues that isolated players in the communication between conferences should pay intermediary fees to non-isolated players. Chapters 6 and 7 discuss the Myerson value and position value for communication situations with fuzzy coalition.