Abstract
Cooperative games with transferable utilities, or simply TUgames, refer to the situations where the revenues created by a coalition of players through cooperation can be freely distributed to the members of the coalition. The fundamental question in cooperative game theory deals with the problem of how much payoff every player should receive. The classical assumption for TUgames states that every coalition is able to form and earn the worth created by cooperation. In the literature, there are several different modifications of TUgames in order to cover the cases where cooperation among the players is restricted. The second chapter of this monograph provides a characterization of the average tree solution for TUgames where the restricted cooperation is represented by a connected cyclefree graph on the set of players. The third chapter considers TUgames for which the restricted cooperation is represented by a directed graph on the set of players and introduces the average covering tree solution and the dominance value for this class of games. Chapter four considers TUgames with restricted cooperation which is represented by a set system on the set of players and introduces the average coalitional tree solution for such structures.
The last two chapters of this monograph belong to the social choice theory literature. Given a set of candidates and a set of an odd number of individuals with preferences on these candidates, pairwise majority comparison of the candidates yields a tournament on the set of candidates. Tournaments are special types of directed graphs which contain an arc between any pair of nodes. The Copeland solution of a tournament is the set of candidates that beat the maximum number of candidates. In chapter five, a new characterization of the Copeland solution is provided that is based on the number of steps in which candidates beat each other. Chapter six of this monograph is on preference aggregation which deals with collective decision making to obtain a social preference. A sophisticated social welfare function is defined as a mapping from profiles of individual preferences into a sophisticated social preference which is a pairwise weighted comparison of alternatives. This chapter provides a characterization of Pareto optimal and pairwise independent sophisticated social welfare functions.
The last two chapters of this monograph belong to the social choice theory literature. Given a set of candidates and a set of an odd number of individuals with preferences on these candidates, pairwise majority comparison of the candidates yields a tournament on the set of candidates. Tournaments are special types of directed graphs which contain an arc between any pair of nodes. The Copeland solution of a tournament is the set of candidates that beat the maximum number of candidates. In chapter five, a new characterization of the Copeland solution is provided that is based on the number of steps in which candidates beat each other. Chapter six of this monograph is on preference aggregation which deals with collective decision making to obtain a social preference. A sophisticated social welfare function is defined as a mapping from profiles of individual preferences into a sophisticated social preference which is a pairwise weighted comparison of alternatives. This chapter provides a characterization of Pareto optimal and pairwise independent sophisticated social welfare functions.
Original language  English 

Qualification  Doctor of Philosophy 
Awarding Institution 

Supervisors/Advisors 

Award date  2 Sept 2014 
Place of Publication  Tilburg 
Publisher  
Print ISBNs  9789056683948 
Publication status  Published  2 Sept 2014 