Contributions to cost allocation problems and scarce resources

Zusammenfassung

This thesis is framed within Game Theory, a Mathematical discipline of great relevance in Economics due to its high degree of applicability in real situations, such as for example, those derived from the allocation of costs and/or benefits or the distribution of scarce resources, among others. One of the great references that gives rise to this branch of Mathematics is the book ”Theory of Games and Economic Behavior” by Oskar Morgenstern and John Von Neumann (Morgenstern and Von Neumann (1953)) to which the Nobel Laureate John Nash contributed with the development of multiple games. The objective of this thesis is not to analyze how the individuals or agents of the game make their decisions, otherwise to provide solutions to the problems proposed using mathematical procedures that allow us to design different mechanisms or rules that satisfy one or a set of properties, also called axioms, that characterize each one of the proposed rules. In this Thesis we present a summary of all the papers that make up this thesis: On how to allocate the fixed cost of transport systems (Estañ et al. (2021a)), Manipulability in the cost allocation of transport systems (Estañ et al. (2020)) and On the difficulty of budget allocation in claims problems with indivisible items and prices (Estañ et al. (2021b)), the first two are focused on the study of cost sharing and the third on the distribution of scarce resources. The first block of this thesis is made up of the papers On how to allocate the fixed cost of transport systems (Estañ et al. (2021a)) and Manipulability in the cost allocation of transport systems (Estañ et al. (2020)). In both, we carry out the axiomatic study of a specific problem of cost distribution, specifically and as a novelty, we focus on the distribution of the fixed cost derived from a straight tram line formed by different stations belonging to a single municipality and also, if we have two adjacent stations that belong to the same municipality, then between them there cannot be any other station that belongs to a different municipality. The second part of this thesis is framed within the problems of allocation of scarce resources. In our paper On the difficulty of budget allocation in claims problems with indivisible items and prices (Estañ et al. (2021b)) we present a new situation: the study of the class of claims problems where we consider that the amount to be divided is perfectly divisible and claims are made for indivisible units of various items. Each item has a price and the available quantity is not enough to cover all the demands at the indicated prices.