Extensions of the Shapley Value and their Characterizations

In this thesis we consider cooperative games with transferable utilities, which are also called TU games. A TU game consists of a finite set of players, and a characteristic function from the set of all possible coalitions to a set of payments. The characteristic function describes how much a set of players can gain by forming a coalition. The main assumption in cooperative game theory is that the grand coalition, i.e., the set containing all involved players, will form. Thus the challenge is how to allocate the payoff of the grand coalition to all players in a fair way. Different definitions of fairness may result in different allocation rules. We aim to characterize some well-known allocation rules (solutions) and their generalizations in different models for cooperative games.