Problemes de repartiment: regles i jocs cooperatius

Abstract

[en] In this work we study claims problems, which happen when there is a certain estate to be distributed and the sum of the claims of all agents is greater than the estate. We study it from an axiomatic point of view, studying the properties of those problems and their distribution rules. We structure the work in 4 parts. Firstly, we present the claims problems and the different distribution rules, paying attention on the 4 most important rules. Besides that, we define some more rules that are not so important, but worth mentioning. The next part is the most important of this work, the characterization of the 4 most important sharing rules. We begin the chapter defining some properties that will later use to make the characterization of them. In the third part, we look at claims problems from a different point of view, from cooperative game theory. We study the relations between cooperative games and claims problems, specifically between distribution rules and point solutions for that kind of games. Finally, we discuss two recent papers where claims problems are used to solve current problems in society. The first tells us about the distribution of the health budget in Catalonia. The second studies the distribution of the permission of CO 2 emissions amongst the different world regions.