Equilibrium play and best response to (Stated) beliefs in constant sum games

We report experimental results on one-shot two person 3x3 constant sum games played by non-economists without previous experience in the laboratory. Although strategically our games are very similar to previous experiments in which game theory predictions fail dramatically, 80% of actions taken in our experiment coincided with the prediction of the unique Nash equilibrium in pure strategies and 73% of actions were best responses to elicited beliefs. We argue how social preferences, presentation effects and belief elicitation procedures may influence how subjects play in simple but non trivial games and explain the diferences we observe with respect to previous work.

Inversion of analytic characteristic functions and infinite convolutions of exponential and Laplace densities

This paper shows that certain quotients of entire functions are characteristic functions. Under some conditions, we provide expressions for the densities of such characteristic functions which turn out to be generalized Dirichlet series which in turn can be expressed as an infinite linear combination of exponential or Laplace densities. We apply these results to several examples.

Generic super-exponential stability of invariant tori in Hamiltonian systems

In this article, we consider solutions starting close to some linearly stable invariant tori in an analytic Hamiltonian system and we prove results of stability for a super-exponentially long interval of time, under generic conditions. The proof combines classical Birkhoff normal forms and a new method to obtain generic Nekhoroshev estimates developed by the author and L. Niederman in another paper. We will mainly focus on the neighbourhood of elliptic fixed points, the other cases being completely similar.

Surface collective oscillations of metal clusters and spheres: Random-phase-approximation sum-rules approach

Using the once and thrice energy-weighted moments of the random-phase-approximation strength function, we have derived compact expressions for the average energy of surface collective oscillations of clusters and spheres of metal atoms. The L=0 volume mode has also been studied. We have carried out quantal and semiclassical calculations for Na and Ag systems in the spherical-jellium approximation. We present a rather thorough discussion of surface diffuseness and quantal size effects on the resonance energies.

Sum rules and short-range correlations in nuclear matter at finite temperature

The nucleon spectral function in nuclear matter fulfills an energy weighted sum rule. Comparing two different realistic potentials, these sum rules are studied for Greens functions that are derived self-consistently within the T matrix approximation at finite temperature.

Sum rules and correlations in asymmetric nuclear matter

The neutron and proton single-particle spectral functions in asymmetric nuclear matter fulfill energy-weighted sum rules. The validity of these sum rules within the self-consistent Green's function approach is investigated. The various contributions to these sum rules and their convergence as a function of energy provide information about correlations induced by the realistic interaction between the nucleons. The study of the sum rules in asymmetric nuclear matter exhibits the isospin dependence of the nucleon-nucleon correlations.

Energy-weighted sum rules for mesons in hot and dense matter

We study energy-weighted sum rules of the pion and kaon propagator in nuclear matter at finite temperature. The sum rules are obtained from matching the Dyson form of the meson propagator with its spectral Lehmann representation at low and high energies. We calculate the sum rules for specific models of the kaon and pion self-energy. The in-medium spectral densities of the K and (K) over bar mesons are obtained from a chiral unitary approach in coupled channels that incorporates the S and P waves of the kaon-nucleon interaction. The pion self-energy is determined from the P-wave coupling to particle-hole and Delta-hole excitations, modified by short-range correlations. The sum rules for the lower-energy weights are fulfilled satisfactorily and reflect the contributions from the different quasiparticle and collective modes of the meson spectral function. We discuss the sensitivity of the sum rules to the distribution of spectral strength and their usefulness as quality tests of model calculations.

On the connectivity of the escaping set for complex exponential Misiurewicz parameters

Let $ E_{\lambda}(z)=\lambda {\rm exp}(z), \lambda\in \mathbb{C}$, be the complex exponential family. For all functions in the family there is a unique asymptotic value at 0 (and no critical values). For a fixed $ \lambda$, the set of points in $ \mathbb{C}$ with orbit tending to infinity is called the escaping set. We prove that the escaping set of $ E_{\lambda}$ with $ \lambda$ Misiurewicz (that is, a parameter for which the orbit of the singular value is strictly preperiodic) is a connected set.

Partial correlation : Network analysis

The final year project came to us as an opportunity to get involved in a topic which has appeared to be attractive during the learning process of majoring in economics: statistics and its application to the analysis of economic data, i.e. econometrics.Moreover, the combination of econometrics and computer science is a very hot topic nowadays, given the Information Technologies boom in the last decades and the consequent exponential increase in the amount of data collected and stored day by day. Data analysts able to deal with Big Data and to find useful results from it are verydemanded in these days and, according to our understanding, the work they do, although sometimes controversial in terms of ethics, is a clear source of value added both for private corporations and the public sector. For these reasons, the essence of this project is the study of a statistical instrument valid for the analysis of large datasets which is directly related to computer science: Partial Correlation Networks.The structure of the project has been determined by our objectives through the development of it. At first, the characteristics of the studied instrument are explained, from the basic ideas up to the features of the model behind it, with the final goal of presenting SPACE model as a tool for estimating interconnections in between elements in large data sets. Afterwards, an illustrated simulation is performed in order to show the power and efficiency of the model presented. And at last, the model is put into practice by analyzing a relatively large data set of real world data, with the objective of assessing whether the proposed statistical instrument is valid and useful when applied to a real multivariate time series. In short, our main goals are to present the model and evaluate if Partial Correlation Network Analysis is an effective, useful instrument and allows finding valuable results from Big Data.As a result, the findings all along this project suggest the Partial Correlation Estimation by Joint Sparse Regression Models approach presented by Peng et al. (2009) to work well under the assumption of sparsity of data. Moreover, partial correlation networks are shown to be a very valid tool to represent cross-sectional interconnections in between elements in large data sets.The scope of this project is however limited, as there are some sections in which deeper analysis would have been appropriate. Considering intertemporal connections in between elements, the choice of the tuning parameter lambda, or a deeper analysis of the results in the real data application are examples of aspects in which this project could be completed.To sum up, the analyzed statistical tool has been proved to be a very useful instrument to find relationships that connect the elements present in a large data set. And after all, partial correlation networks allow the owner of this set to observe and analyze the existing linkages that could have been omitted otherwise.

Classical line shapes based on analytical solutions of bimolecular trajectories in collision induced emission. II. Reactive collisions

The classical theory of collision induced emission (CIE) from pairs of dissimilar rare gas atoms was developed in Paper I [D. Reguera and G. Birnbaum, J. Chem. Phys. 125, 184304 (2006)] from a knowledge of the straight line collision trajectory and the assumption that the magnitude of the dipole could be represented by an exponential function of the inter-nuclear distance. This theory is extended here to deal with other functional forms of the induced dipole as revealed by ab initio calculations. Accurate analytical expression for the CIE can be obtained by least square fitting of the ab initio values of the dipole as a function of inter-atomic separation using a sum of exponentials and then proceeding as in Paper I. However, we also show how the multi-exponential fit can be replaced by a simpler fit using only two analytic functions. Our analysis is applied to the polar molecules HF and HBr. Unlike the rare gas atoms considered previously, these atomic pairs form stable bound diatomic molecules. We show that, interestingly, the spectra of these reactive molecules are characterized by the presence of multiple peaks. We also discuss the CIE arising from half collisions in excited electronic states, which in principle could be probed in photo-dissociation experiments.

Computational explorations in Thompson's group F

Here we describe the results of some computational explorations in Thompson's group F. We describe experiments to estimate the cogrowth of F with respect to its standard finite generating set, designed to address the subtle and difficult question whether or not Thompson's group is amenable. We also describe experiments to estimate the exponential growth rate of F and the rate of escape of symmetric random walks with respect to the standard generating set.

Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibriaThe Patterson-Sullivan embedding and minimal volume entropy for outer space

We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic thermostat by means of the contractivity of a suitable metric in the set of probability measures. Existence, uniqueness, boundedness of moments and regularity of a steady state are derived from this basic property. The solutions of the kinetic model are proved to converge exponentially as t→ ∞ to this diffusive equilibrium in this distance metrizing the weak convergence of measures. Then, we prove a uniform bound in time on Sobolev norms of the solution, provided the initial data has a finite norm in the corresponding Sobolev space. These results are then combined, using interpolation inequalities, to obtain exponential convergence to the diffusive equilibrium in the strong L¹-norm, as well as various Sobolev norms.

Double implementation in a market for indivisible goods with a price constraint

I consider the problem of assigning agents to objects where each agent must pay the price of the object he gets and prices must sum to a given number. The objective is to select an assignment-price pair that is envy-free with respect to the true preferences. I prove that the proposed mechanism will implement both in Nash and strong Nash the set of envy-free allocations. The distinguishing feature of the mechanism is that it treats the announced preferences as the true ones and selects an envy-free allocation with respect to the announced preferences.

Reference prices: the spanish way

The aim of this paper is to analyse the effects of recent regulatory reforms that Spanish Health Authorities have implemented in the pharmaceutical market: the introduction of a reference price system together with the promotion of generic drugs. The main objectives of these two reforms are to increase price competition and, ultimately, reduce pharmaceutical costs. Before the introduction of reference prices, consumers had to pay a fixed copayment of the price of whatever drug purchased. With the introduction of such system, the situation differs in the following way: if (s)he buys the more expensive branded drug, then (s)he pays a sum of two elements: the copayment associated to the reference price plus the difference between the price of this good and the reference price. However, if the consumer decides to buy the generic alternative, with price lower than the reference price, then (s)he has to pay the same copayment as before. We show that the introduction of a reference price system together with the promotion of generic drugs increase price competition and lower pharmaceutical costs only if the reference price is set in a certain interval. Also profits for the duopolists might be reduced. These results are due to the opposing effects that reference prices have on branded and generic producers respectively.