Time consistent Pareto solutions in common access resource gameswith asymmetric players

In the analysis of equilibrium policies in a di erential game, if agents have different time preference rates, the cooperative (Pareto optimum) solution obtained by applying the Pontryagin's Maximum Principle becomes time inconsistent. In this work we derive a set of dynamic programming equations (in discrete and continuous time) whose solutions are time consistent equilibrium rules for N-player cooperative di erential games in which agents di er in their instantaneous utility functions and also in their discount rates of time preference. The results are applied to the study of a cake-eating problem describing the management of a common property exhaustible natural resource. The extension of the results to a simple common property renewable natural resource model in in nite horizon is also discussed.

Heterogeneous discounting in consumption-investment problems. Time consistent solutions

[cat] En aquest treball s'analitza un model estocàstic en temps continu en el que l'agent decisor descompta les utilitats instantànies i la funció final amb taxes de preferència temporal constants però diferents. En aquest context es poden modelitzar problemes en els quals, quan el temps s'acosta al moment final, la valoració de la funció final incrementa en comparació amb les utilitats instantànies. Aquest tipus d'asimetria no es pot descriure ni amb un descompte estàndard ni amb un variable. Per tal d'obtenir solucions consistents temporalment es deriva l'equació de programació dinàmica estocàstica, les solucions de la qual són equilibris Markovians. Per a aquest tipus de preferències temporals, s'estudia el model clàssic de consum i inversió (Merton, 1971) per a les funcions d'utilitat del tipus CRRA i CARA, comparant els equilibris Markovians amb les solucions inconsistents temporalment. Finalment es discuteix la introducció del temps final aleatori.

Aggregate monotonic stable single-valued solutions for cooperative games

[cat] En aquest treball caracteritzem les solucions puntuals de jocs cooperatius d'utilitat transferible que compleixen selecció del core i monotonia agregada. També mostrem que aquestes dues propietats són compatibles amb la individualitat racional, la propietat del jugador fals i la propietat de simetria. Finalment, caracteritzem les solucions puntuals que compleixen les cinc propietats a l'hora.

Coalitionally monotonic set-solutions for cooperative TU games

A static comparative study on set-solutions for cooperative TU games is carried out. The analysis focuses on studying the compatibility between two classical and reasonable properties introduced by Young (1985) in the context of single valued solutions, namely core-selection and coalitional monotonicity. As the main result, it is showed that coalitional monotonicity is not only incompatible with the core-selection property but also with the bargaining-selection property. This new impossibility result reinforces the tradeoff between these kinds of interesting and intuitive economic properties. Positive results about compatibility between desirable economic properties are given replacing the core selection requirement by the core-extension property.

Nucleation in supersaturated solutions 3He in 4He at negative pressure.

Depending on the 3He concentration, thermal nucleation in 3-4He supersaturated liquid mixtures at negative pressures may be originated either by bubble or by 3rich drop formation. We have investigated this phenomenon within a density-functional approach, determining the regions in the pressure¿3He-concentration plane where bubbles or drops likely drive the nucleation process. As an illustrative example, we also give the homogeneous nucleation pressure corresponding to 50 and 100 mK temperature.

Classical solutions of the leading-logarithm approximation with non-trivial topology

Exact solutions of the classical equations corresponding to the leading-logarithm approximation are obtained. They are classified by an (integer) topological number.

Generalized Weyl solutions

It was shown by Weyl that the general static axisymmetric solution of the vacuum Einstein equations in four dimensions is given in terms of a single axisymmetric solution of the Laplace equation in three-dimensional flat space. Weyls construction is generalized here to arbitrary dimension D>~4. The general solution of the D-dimensional vacuum Einstein equations that admits D-2 orthogonal commuting non-null Killing vector fields is given either in terms of D-3 independent axisymmetric solutions of Laplaces equation in three-dimensional flat space or by D-4 independent solutions of Laplaces equation in two-dimensional flat space. Explicit examples of new solutions are given. These include a five-dimensional asymptotically flat black ring with an event horizon of topology S1S2 held in equilibrium by a conical singularity in the form of a disk.

General clas of inhomogeneous perfect-fluid solutions

We present a general class of solutions to Einstein's field equations with two spacelike commuting Killing vectors by assuming the separation of variables of the metric components. The solutions can be interpreted as inhomogeneous cosmological models. We show that the singularity structure of the solutions varies depending on the different particular choices of the parameters and metric functions. There exist solutions with a universal big-bang singularity, solutions with timelike singularities in the Weyl tensor only, solutions with singularities in both the Ricci and the Weyl tensors, and also singularity-free solutions. We prove that the singularity-free solutions have a well-defined cylindrical symmetry and that they are generalizations of other singularity-free solutions obtained recently.

Soliton solutions and cosmological gravitational waves

We examine plane-symmetric cosmological solutions to Einstein's equations which can be generated by the "soliton" technique, using the homogeneous Bianchi solutions as seeds and arbitrary numbers of real or complex poles. In some circumstances, these solutions can be interpreted as "incipient" gravitational waves on the Bianchi background. At early times they look like nonlinear inhomogeneities propagating at nearly the speed of light ("gravisolitons"), while at late times they look like cosmological gravitational waves.

Multisoliton solutions to Einstein's equations

We discuss a multisoliton solution to Einsteins equations in vacuum. The solution is interpreted as many gravitational solitons propagating and colliding on a homogeneous cosmological background. Following a previous letter, we characterize the solitons by their localizability and by their peculiar properties under collisions. Furthermore, we define an associated frame-dependent velocity field which illustrates the solitonic character of these gravitational solitons in the classical sense.

Towards and ab initio description of magnetism in ionic solids

The physical contributions to the KNiF3 magnetic exchange coupling integral have been obtained from specially designed ab initio cluster model calculations. Three important mechanisms have been identified. These are the delocalization of the magnetic orbitals into the anion p band, the variational contribution of the second-order interactions, and the many-body terms hidden in the two-body operator and the Heisenberg Hamiltonian.