On the Difficulty of Budget Allocation in Claims Problems with Indivisible Items and Prices

First of all, the authors thank the Associate Editor and three anonymous Reviewers for their time to review our paper and also for their for their incisive comments and suggestions which have been very helpful to improve the contents of the paper. The authors gratefully acknowledge financial support from the Ministerio de Ciencia, Innovacion y Universidades (MCIU), the Agencia Estatal de Investigacion (AEI) and the Fondo Europeo de Desarrollo Regional (FEDER) under the project PGC2018-097965-B-I00 and the Spanish Ministry of Science under Project ECO2017-86245-P, as well as Junta de Andalucia under Projects Grupos PAIDI SEJ426 and project P18-FR-2933.In this paper we study the class of claims problems where the amount to be divided is perfectly divisible and claims are made on indivisible units of several items. Each item has a price, and the available amount falls short to be able to cover all the claims at the given prices. We propose several properties that may be of interest in this particular framework. These properties represent the common principles of fairness, efficiency, and non-manipulability by merging or splitting. Efficiency is our focal principle, which is formalized by means of two axioms: non-wastefulness and Pareto efficiency. We show that some combinations of the properties we consider are compatible, others are not.Ministerio de Ciencia, Innovacion y Universidades (MCIU)Agencia Estatal de Investigacion (AEI)European Commission PGC2018-097965-B-I00Spanish Government ECO2017-86245-PJunta de Andalucia PAIDI SEJ426 P18-FR-293

Decentralized clearing in financial networks

We consider a situation in which agents have mutual claims on each other, summarized in a liability matrix. Agents' assets might be insufficient to satisfy their liabilities leading to defaults. In case of default, bankruptcy rules are used to specify the way agents are going to be rationed. A clearing payment matrix is a payment matrix consistent with the prevailing bankruptcy rules that satisfies limited liability and priority of creditors. Since clearing payment matrices and the corresponding values of equity are not uniquely determined, we provide bounds on the possible levels equity can take. Unlike the existing literature, which studies centralized clearing procedures, we introduce a large class of decentralized clearing processes. We show the convergence of any such process in finitely many iterations to the least clearing payment matrix. When the unit of account is sufficiently small, all decentralized clearing processes lead essentially to the same value of equity as a centralized clearing procedure. As a policy implication, it is not necessary to collect and process all the sensitive data of all the agents simultaneously and run a centralized clearing procedure

Contributions to cost allocation problems and scarce resources

Esta tesis est a enmarcada dentro de la Teor a de Juegos, disciplina Matem atica de gran relevancia en Econom a por su alto grado de aplicabilidad en situaciones reales, como por ejemplo las derivadas del reparto de costes y/o bene cios o la distribuci on de recursos escasos, entre muchas otras. Una de las grandes referencias que da origen a esta rama de las Matem aticas es el libro "Theory of Games and Economic Behavior" de Oskar Morgenstern y John Von Neumann (Morgenstern and Von Neumann (1953)) al cual contribuy o de manera seminal con el desarrollo de los juegos m ultiples el Premio Nobel John Nash. El objetivo de esta tesis no es analizar c omo los individuos o agentes del juego toman sus decisiones sino proporcionar soluciones a los problemas planteados empleando procedimientos matem aticos que nos permiten dise~nar diferentes mecanismos o reglas que satisfacen uno o un conjunto de propiedades, tambi en llamadas axiomas, que caracterizan cada una de las reglas planteadas.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 bene ts 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 di erent mechanisms or rules that satisfy one or a set of properties, also called axioms, that characterize each one of the proposed rules