Documents de treball (Matemàtica Econòmica, Financera i Actuarial)
URI permanent per a aquesta col·leccióhttps://hdl.handle.net/2445/12560
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Document de treballAxioms for the optimal stable rules and fair-division rules in a multiple-partners job market [WP](Universitat de Barcelona. Facultat d'Economia i Empresa, 2022) Domènech i Gironell, Gerard; Núñez, Marina (Núñez Oliva)In the multiple-partners job market, introduced in (Sotomayor, 1992), each firm can hire several workers and each worker can be hired by several firms, up to a given quota. We show that, in contrast to what happens in the simple assignment game, in this extension, the firms-optimal stable rules are neither valuation monotonic nor pairwise monotonic. However, we show that the firms-optimal stable rules satisfy a weaker property, what we call firm covariance, and that this property characterizes these rules among all stable rules. This property allows us to shed some light on how firms can (and cannot) manipulate the firms-optimal stable rules. In particular, we show that firms cannot manipulate them by constantly over-reporting their valuations. Analogous results hold when focusing on the workers. Finally, we extend to the multiple-partners market a known characterization of the fair-division rules on the domain of simple assignment games.- Document de treballStable cores in information graph games [WP](Universitat de Barcelona. Facultat d'Economia i Empresa, 2020) Núñez, Marina (Núñez Oliva); Vidal-Puga, JuanStable cores in information graph games Abstract: In an information graph situation, some agents that are connected by an undirected graph can share with no cost some information or technology that can also be obtained from a source. If an agent is not connected to an informed player, this agent pays a unitary cost to obtain this technology. A coalitional cost game can be defined from this situation, and the core of this game is known to be non- empty. We prove that the core of an information graph game is a von Neumann-Morgenstern stable set if and only if the graph is cycle- complete, or equivalently if the information graph game is concave. When the graph is not cycle-complete, whether there always exists a stable set is an open question. In this regard, we show that if the information graph consists of a ring that contains the source, then a stable set always exists and it is the core of a related information graph situation where one edge has been deleted.
- Document de treballContinuous-time Optimal Pension Indexing in Pay-as-You-Go Systems(Universitat de Barcelona. Facultat d'Economia i Empresa, 2020) Roch, OriolAgeing population and economic crisis have placed pay-as-you-go pension systems in need of mechanisms to ensure its financial stability. In this paper, we consider optimal indexing of pensions as an instrument to cope with the financial imbalances typically found in these systems. Using dynamic programming techniques in a stochastic continuous-time framework, we compute the optimal pension index and portfolio strategy that best target indexing and liquidity objectives determined by the government. A numerical example is provided to illustrate the results
- Document de treballIntroducing media in a model of electoral competition with candidate quality(Universitat de Barcelona. Facultat d'Economia i Empresa, 2020) Domènech i Gironell, GerardThis work proposes and studies a two candidate model of electoral competition with candidate quality and media. The role of media is to inform voters about the quality of each candidate. We assume that there are two non-strategic media outlets, each one with a different ideal policy (there is a leftist media outlet and a rightist one), and that both of them transmit lower quality for a candidate the further from their ideal policy the policy the candidate proposes is. We also assume that the rightist media outlet has greater coverage, in the sense that it informs neutral voters and voters slightly on the left side of the political spectrum. We study the model under the classical assumption of risk-averse voters. Classical results concerning PSNE generally hold with a "media bias". We extend and characterize in our setting the MSNE found in Aragonés and Xefteris (2012), which sometimes fails to exist in our model.
- Document de treballAnálisis cuantitativo de productos en España para licuar el patrimonio en la tercera edad: rentas vitalicias e hipotecas inversas(2020-03-06) Bosch Príncep, Manuela; Claramunt Bielsa, M. MercèLas recientes reformas del sistema público de pensiones en España tendrán como consecuencia, en la mayoría de los casos, la disminución de los importes de las pensiones de jubilación. Frente a esta situación, parece de sentido común que se contemplen posibilidades de disponer de unos ingresos adicionales a los de la pensión pública. Si se tiene un plazo de tiempo suficiente, una opción es ahorrar con el objetivo de que llegado el momento de la jubilación se haya constituido el capital suficiente. Otra opción para las personas que no tengan margen de maniobra, pero en cambio dispongan de inmuebles, es buscar alternativas que les permitan licuar los inmuebles para conseguir el mismo objetivo. En este trabajo, centramos la atención en la segunda opción y analizamos dos instrumentos del mercado financiero y asegurador para obtener liquidez a partir de los bienes inmuebles: las rentas vitalicias aseguradas inmobiliarias y las hipotecas inversas. Adicionalmente a la definición y posterior tarificación de cada producto, en este trabajo se incluyen los efectos fiscales, y se realiza una comparativa cuantitativa de la renta resultante para el contratante del producto y sus herederos.
- Document de treballOn Convexity in Games with Externalities(Universitat de Barcelona. Facultat d'Economia i Empresa, 2019) Alonso-Meijide, José Mª; Álvarez-Mozos, Mikel; Fiestras-Janeiro, M. Gloria, 1962-; Jiménez-Losada, AndrésWe introduce new notions of superadditivity and convexity for games with coalitional externalities. We show parallel results to the classic ones for transferable utility games without externalities. In superadditive games the grand coalition is the most efficient organization of agents. The convexity of a game is equivalent to having non decreasing contributions to larger embedded coalitions. We also see that convex games can only have negative externalities
- Document de treballAssortative multisided assignment games. The extreme core points [WP](Universitat de Barcelona. Facultat d'Economia i Empresa, 2019) Martínez de Albéniz, F. Javier; Rafels, Carles; Ybern, NeusWe analyze assortative multisided assignment games, following Sherstyuk (1999) and Martínez-de-Albéniz et al. (2019). In them players’ abilities are complementary across types (i.e. supermodular), and also the output of the essential coalitions is increasing depending on types. We study the extreme core points and show a simple mechanism to compute all of them. In this way we describe the whole core. This mechanism works from the original data array and the maximum number of extreme core points is obtained.
- Document de treballA new order on embedded coalitions: Properties and Applications(Universitat de Barcelona. Facultat d'Economia i Empresa, 2019) Alonso-Meijide, José Mª; Álvarez-Mozos, Mikel; Fiestras-Janeiro, M. Gloria, 1962-; Jiménez-Losada, AndrésGiven a finite set of agents, an embedded coalition consists of a coalition and a partition of the rest of agents. We study a partial order on the set of embedded coalitions of a finite set of agents. An embedded coalition precedes another one if the first coalition is contained in the second and the second partition equals the first one after removing the agents in the second coalition. This poset is not a lattice. We describe the maximal lower bounds and minimal upper bounds of a finite subset, whenever they exist. It is a graded poset and we are able to count the number of elements at a given level as well as the total number of chains. The study of this structure allows us to derive results for games with externalities. In particular, we introduce a new concept of convexity and show that it is equivalent to having non-decreasing contributions to embedded coalitions of increasing size.
- Document de treballThe nucleolus of the assignment game. Structure of the family(Universitat de Barcelona. Facultat d'Economia i Empresa, 2018) Martínez de Albéniz, F. Javier; Rafels, Carles; Ybern, NeusWe show that the family of assignment matrices which give rise to the same nucleolus forms a compact join-semilattice with one maximal element. The above family is in general not a convex set, but path-connected.
- Document de treballStrategic investment decisions under the nuclear power debate in Belgium [WP](Universitat de Barcelona. Facultat d'Economia i Empresa, 2018) Frutos Cachorro, Julia de; Willeghems, Gwen; Buysse, JeroenIn view of the current nuclear power debate in Belgium, we analyze how uncertainty about a nuclear phase-out, coupled with the implementation of renewable energy subsidies and nuclear taxes, affects investment capacity and productivity decisions by Belgian electricity suppliers. To achieve this goal, considering the key characteristics of the Belgian market, we build a Stackelberg closed-loop (two-stage) equilibrium model in which investment decisions are made in a first stage under uncertainty regarding a nuclear phase-out, and productivity decisions are subsequently made in a second stage in a c ertainty environment. Our analysis indicates that, regardless of subsidies, an increase in the probability of nuclear license extension results in lower levels of investment - primarily in renewable energy -, lower total production and a higher electricity price. We also show that the implementation of renewable energy subsidies reduces the effect of an increase in probability of nuclear license extension on producer’s decisions regarding expanded capacity and on total profits in the market.
- Document de treballThe family of lattice structure values for games with externalities(Universitat de Barcelona. Facultat d'Economia i Empresa, 2018) Alonso-Meijide, José Mª; Álvarez-Mozos, Mikel; Fiestras-Janeiro, M. Gloria, 1962-; Jiménez-Losada, AndrésWe propose and characterize a new family of Shapley values for games with coalitional externalities. To define it we generalize the concept of marginal contribution by using a lattice structure on the set of embedded coalitions. The family of lattice structure values is characterized by extensions of Shapley's axioms: efficiency, additivity, symmetry, and the null player property. The first three axioms have widely accepted generalizations to the framework of games with externalities. However, different concepts of null players have been proposed in the literature and we contribute to this debate with a new one. The null player property that we use is weaker than the others. Finally, we present one particular value of the family, new in the literature, which delivers balanced payoffs and characterize it by two additional properties.
- Document de treballValuation monotonicity, fairness and stability in assignment problems [WP](Universitat de Barcelona. Facultat d'Economia i Empresa, 2018) Van den Brink, René; Núñez, Marina (Núñez Oliva); Robles Jiménez, Francisco JavierIn this paper, we investigate the possibility of having stable rules for twosided markets with transferable utility, that satisfy some valuation monotonicity and fairness axioms. Valuation fairness requires that changing the valuation of a buyer for the object of a seller leads to equal changes in the payoffs of this buyer and seller. This is satisfied by the Shapley value, but is incompatible with stability. A main goal in this paper is to weaken valuation fairness in such a way that it is compatible with stability. It turns out that requiring equal changes only for buyers and sellers that are matched to each other before as well as after the change, is compatible with stability. In fact, we show that the only stable rule that satisfies weak valuation fairness is the well-known fair division rule which is obtained as the average of the buyers-optimal and the sellersoptimal payoff vectors. Our second goal is to characterize these two extreme rules by valuation monotonicity axioms. We show that the buyers-optimal (respectively sellersoptimal) stable rule is char- acterized as the only stable rule that satisfies buyervaluation monotonicity which requires that a buyer cannot be better off by weakly decreasing his/her valuations for all objects, as long as he is assigned the same object as before (respectively object-valuation antimonotonicity which requires that a buyer cannot be worse off when all buyers weakly decrease their valuations for the object that is assigned to this specific buyer, as long as this buyer is assigned the same object as before). Finally, adding a consistency axiom, the two optimal rules are characterized in the general domain of allocation rules for two-sided assignment markets with a variable population.
- Document de treballSolving Becker's assortative assignments and extensions(Universitat de Barcelona. Facultat d'Economia i Empresa, 2018) Martínez de Albéniz, F. Javier; Rafels, Carles; Ybern, NeusWe analyze assortative assignment games, introduced in Becker (1973) and Eriksson et al. (2000). We study the extreme core points and show an easy way to compute them. We find a natural solution for these games. It coincides with several well-known point solutions, the median stable utility solution (Schwarz and Yenmez, 2011) and the nucleolus (Schmeidler, 1969).We also analyze the behavior of the Shapley value. We finish with some extensions, where some hypotheses are relaxed.
- Document de treballThe incentive core in co-investment problems(Universitat de Barcelona. Facultat d'Economia i Empresa, 2017) Izquierdo Aznar, Josep Maria; Rafels, CarlesWe study resource-monotonicity properties of core allocations in coinvestment problems: those where a set of agents pool their endowments of a certain resource or input in order to obtain a joint surplus or output that must be allocated among the agents. We analyze whether agents have incentives to raise their initial contribution (resource-monotonicity). We focus not only on looking for potential incentives to agents who raise their contributions, but also in not harming the payoffs to the rest of agents (strong monotonicity property). A necessary and suficient condition to fulfill this property is stated and proved. We also provide a subclass of coinvestment problems for which any core allocation satisfies the aforementioned strong resource-monotonicity property. Moreover, we introduce the subset of core allocations satisfying this condition, namely the incentive core.
- Document de treballGames with Graph Restricted Communication and Levels Structure of Cooperation(Universitat de Barcelona. Facultat d'Economia i Empresa, 2017) Tejada, Oriol; Álvarez-Mozos, MikelWe analyze surplus allocation problems where cooperation between agents is restricted both by a communication graph and by a sequence of embedded partitions of the agent set. For this type of problem, we define and characterize two new vàlues extending the Shapley value and the Banzhaf value respectively. Our results enable the axiomatic comparison between the two values and provide some basic insights for the analysis of fair resource allocation in nowadays fully integrated societies.
- Document de treballMulti-sided assignment games on m-partite graphs [WP](Universitat de Barcelona. Facultat d'Economia i Empresa, 2017) Atay, Ata; Núñez, Marina (Núñez Oliva)We consider a multi-sided assignment game with the following characteristics: (a) the agents are organized in m sectors that are connected by a graph that induces a weighted m-partite graph on the set of agents, (b) a basic coalition is formed by agents from different connected sectors, and (c) the worth of a basic coalition is the addition of the weights of all its pairs that belong to connected sectors. We provide a sufficient condition on the weights to guarantee balancedness of the related multi-sided assignment game. Moreover, when the graph on the sectors is cycle-free, we prove the game is strongly balanced and the core is described by means of the cores of the underlying two-sided assignment games associated with the edges of this graph. Moreover, once selected a spanning tree of the cycle-free graph on the sectors, the equivalence between core and competitive equilibria is established.
- Document de treballSome structural properties of a lattice of embedded coalitions [WP](Universitat de Barcelona. Facultat d'Economia i Empresa, 2016) Alonso-Meijide, José Mª; Álvarez-Mozos, Mikel; Fiestras-Janeiro, M. Gloria, 1962-; Jiménez-Losada, AndrésIn this paper we investigate some structural properties of the order on the set of embedded coalitions outlined in de Clippel and Serrano (2008). Besides, we characterize the scalars associated to the basis they proposed of the vector space of partition function form games.
- Document de treballAn alternative proof of the characterization of core stability for the assignment game [WP](Universitat de Barcelona. Facultat d'Economia i Empresa, 2016) Atay, AtaSolymosi and Raghavan (2001) characterize the stability of the core of the assignment game by means of a property of the valuation matrix. They show that the core of an assignment game is a von Neumann-Morgenstern stable set if and only if its valuation matrix has a dominant diagonal. Their proof makes use of some graphtheoretical tools, while the present proof relies on the notion of buyer-seller exact representative in Núñez and Rafels (2002)
- Document de treballConstrained multi-issue rationing problems(Universitat de Barcelona. Facultat d'Economia i Empresa, 2016) Izquierdo Aznar, Josep Maria; Timoner Lledó, PereWe study a variant of the multi-issue rationing model, where agents claim for several issues. In this variant, the available amount of resource intended for each issue is constrained to an amount fixed a priori according to exogenous criteria. The aim is to distribute the amount corresponding to each issue taking into account the allocation for the rest of issues (issue-allocation interdependence). We name these problems constrained multi-issue allocation situations (CMIA). In order to tackle the solution to these problems, we first reinterpret some single-issue egalitarian rationing rules as a minimization program based on the idea of finding the feasible allocation as close as possible to a specific reference point. We extend this family of egalitarian rules to the CMIA framework. In particular, we extend the constrained equal awards rule, the constrained equal losses rule and the reverse Talmud rule to the multi-issue rationing setting, which turn out to be particular cases of a family of rules, namely the extended α-egalitarian family. This family is analysed and characterized by using consistency principles (over agents and over issues) and a property based on the Lorenz dominance criterion.
- Document de treballDecentralized rationing problems [WP](Universitat de Barcelona. Facultat d'Economia i Empresa, 2016) Izquierdo Aznar, Josep Maria; Timoner Lledó, PereDecentralized rationing problems are those in which the resource is not directly assigned to agents, but first allocated to groups of agents and then divided among their members. Within this framework, we define extensions of the constrained equal awards, the constrained equal losses and the proportional rules. We show that the first two rules do not preserve certain essential properties and prove the conditions under which both rules do preserve those properties. We characterize the extension of the proportional rule as the only solution that satisfies individual equal treatment of equals. We prove that the proportional rule is the only solution that assigns the same allocation regardless of whether the resource is distributed directly to agents or in a decentralized manner (with agents grouped). Finally, we analyse a strategic game based on decentralized rationing problems in which agents can move freely across groups to submit their claims.