A Differentiable Homotopy to Compute Nash Equilibria of n-Person Games

The literature on the computation of Nash equilibria in n-person games is dominated by simplicial methods. This paper is the first to introduce a globally convergent algorithm that fully exploits the differentiability present in the problem. It presents an everywhere differentiable homotopy to do the computations. The homotopy path can therefore be followed by several numerical techniques. Moreover, instead of computing some Nash equilibrium, the algorithm is constructed in such a way that it computes the Nash equilibrium selected by the tracing procedure of Harsanyi and Selten. As a by-product of our proofs it follows that for a generic game the tracing procedure defines an unique feasible path. The numerical performance of the algorithm is illustrated by means of several examples.microeconomics ;

Tactile spatial attention enhances gamma-band activity in somatosensory cortex and reduces low-frequency activity in parieto-occipital areas.

We investigated the effects of spatial-selective attention on oscillatory neuronal dynamics in a tactile delayed-match-to-sample task. Whole-head magnetoencephalography was recorded in healthy subjects while dot patterns were presented to their index fingers using Braille stimulators. The subjects’ task was to report the reoccurrence of an initially presented sample pattern in a series of up to eight test stimuli that were presented unpredictably to their right or left index finger. Attention was cued to one side (finger) at the beginning of each trial, and subjects performed the task at the attended side, ignoring the unattended side. After stimulation, high-frequency gamma-band activity (60 –95 Hz) in presumed primary somatosensory cortex (S1) was enhanced, whereas alpha- and beta-band activity were suppressed in somatosensory and occipital areas and then rebounded. Interestingly, despite the absence of any visual stimulation, we also found time-locked activation of medial occipital, presumably visual, cortex. Most relevant, spatial tactile attention enhanced stimulus-induced gamma-band activity in brain regions consistent with contralateral S1 and deepened and prolonged the stimulus induced suppression of beta- and alpha-band activity, maximal in parieto-occipital cortex. Additionally, the beta rebound over contralateral sensorimotor areas was suppressed. Wehypothesize that spatial-selective attention enhances the saliency of sensory representations by synchronizing neuronal responses in early somatosensory cortex and thereby enhancing their impact on downstream areas and facilitating interareal processing. Furthermore, processing of tactile patterns also seems to recruit visual cortex and this even more so for attended compared with unattended stimuli

Standardization and application of microsatellite markers for variety identification in tomato and wheat

The present study is part of a EU project that aims to demonstrate the technical viability of STMS markers for variety identification. As examples two important European crop species, tomato and wheat were chosen. Initially, about 30-40 STMS markers were used to identify a set of 20 good markers per crop and to standardise the methodology and the interpretation of the results in different laboratories. Several systems were used for the detection of STMS polymorphisms. The selected STMS markers are being tested on 500 varieties of each species and databases are being constructed. The first comparisons of data generated by the different laboratories revealed a high degree of agreement. The causes of discrepancies between duplicate samples analysed in different laboratories and precautions to prevent them, are discussed

"Better Safe than Sorry" - Individual Risk-free Pension Schemes in the European Union - Macroeconomic Benefits, the Mobile Working Citizen's Perspective and Why Nots

Variations between the diverse pension systems in the member states of the European Union hamper labour market mobility, across country borders but also within the countries of the European Union. From a macroeconomic perspective, and in the light of demographic pressure, this paper argues that allowing individual instead of collective pension building would greatly improve labour market flexibility and thus enhance the functioning of the monetary union. I argue that working citizens would benefit, for three reasons, from pension saving in a risk-free savings account. First, citizens would have a clear picture of the accumulation of their own pension savings throughout their working life. Second, they would pay hardly any extra costs and, third, once retired they would not be subject to the whims of government or other pension fund managers. This paper investigates the feasibility of individual pension building under various parameter settings by calculating the pension saved during a working life and the pension dis-saved after retirement. The findings show that there are no reasons why the European Union and individual member states should not allow individual risk-free pension savings accounts. This would have macroeconomic benefits and provide a solid pension provision that can enhance mobility, instead of engaging workers in different mandatory collective pension schemes that exist around in the European Union

Polaron effects in electron channels on a helium film

Using the Feynman path-integral formalism we study the polaron effects in quantum wires above a liquid helium film. The electron interacts with two-dimensional (2D) surface phonons, i.e. ripplons, and is confined in one dimension (1D) by an harmonic potential. The obtained results are valid for arbitrary temperature ($T$), electron-phonon coupling strength ($\alpha$), and lateral confinement ($\omega_{0}$). Analytical and numerical results are obtained for limiting cases of $T$, $\alpha$, and $\omega_{0}$. We found the surprising result that reducing the electron motion from 2D to quasi-1D makes the self-trapping transition more continuous.Comment: 6 pages, 7 figures, submitted to Phys. Rev.

Classical double-layer atoms: artificial molecules

The groundstate configuration and the eigenmodes of two parallel two-dimensional classical atoms are obtained as function of the inter-atomic distance (d). The classical particles are confined by identical harmonic wells and repel each other through a Coulomb potential. As function of d we find several structural transitions which are of first or second order. For first (second) order transitions the first (second) derivative of the energy with respect to d is discontinuous, the radial position of the particles changes discontinuously (continuously) and the frequency of the eigenmodes exhibit a jump (one mode becomes soft, i.e. its frequency becomes zero).Comment: 4 pages, RevTex, 5 ps figures, to appear in Phys.Rev.Let

Planar cyclotron motion in unidirectional superlattices defined by strong magnetic and electric fields: Traces of classical orbits in the energy spectrum

We compare the quantum and the classical description of the two-dimensional motion of electrons subjected to a perpendicular magnetic field and a one-dimensional lateral superlattice defined by spatially periodic magnetic and electric fields of large amplitudes. We explain in detail the complicated energy spectra, consisting of superimposed branches of strong and of weak dispersion, by the correspondence between the respective eigenstates and the ``channeled'' and ``drifting'' orbits of the classical description.Comment: 11 pages, 11 figures, to appear in Physical Review