This thesis presents theories of allocation problems, starting with the basic definitions of an allocation problem and ending with the characterization of the methods, which can be used as solutions to these problems. The five sections of this thesis start with the first part introducing the chosen subject, explaining what motivated me to this choice and to what length and depth I chose to delve into the subject. The second section is divided into two chapters; the first chapter deals with the basic definitions of allocation problems and the second chapter shows some of the classes, allocation problems can belong to if they fulfill certain properties. The third section belongs to allocation rules, which are seen as the solutions to the allocation problems. Like the second section, the third section is divided into two chapters, where the first chapter explains four known allocation rules and closes with an allocation rule of my own invention, dubbed “the alternative allocation rule”. The second chapter of this section explains properties of allocation rules which are chosen with the four known allocation rules in mind. The third chapter explains different kinds of monotonicity of allocation rules. Classes of problems and properties of allocation rules are shown and proved in connection with the Shapley allocation rule and the alternative allocation rule in the fourth section to characterize them. These two allocation rules are compared according to which properties they meet to get a picture of how they differ exactly. The last and fifth section closes this thesis with remarks on how the alternative allocation rule fared and discusses which theories of allocation problems could be explored to further characterize the alternative allocation rule.
|Educations||MSc in Mathematics , (Graduate Programme) Final Thesis|
|Number of pages||76|