Determination of sequential best replies in n-player games by Genetic Algorithms

An iterative algorithm for establishing the Nash Equilibrium in pure strategies (NE) is proposed and tested in Cournot Game models. The algorithm is based on the convergence of sequential best responses and the utilization of a genetic algorithm for determining each player's best response to a given strategy profile of its opponents. An extra outer loop is used, to address the problem of finite accuracy, which is inherent in genetic algorithms, since the set of feasible values in such an algorithm is finite. The algorithm is tested in five Cournot models, three of which have convergent best replies sequence, one with divergent sequential best replies and one with \local NE traps"(Son and Baldick 2004), where classical local search algorithms fail to identify the Nash Equilibrium. After a series of simulations, we conclude that the algorithm proposed converges to the Nash Equilibrium, with any level of accuracy needed, in all but the case where the sequential best replies process diverges.Genetic Algorithms, Cournot oligopoly, Best Response, Nash Equilibrium

Possible solution of the Coriolis attenuation problem

The most consistently useful simple model for the study of odd deformed nuclei, the particle-rotor model (strong coupling limit of the core-particle coupling model) has nevertheless been beset by a long-standing problem: It is necessary in many cases to introduce an ad hoc parameter that reduces the size of the Coriolis interaction coupling the collective and single-particle motions. Of the numerous suggestions put forward for the origin of this supplementary interaction, none of those actually tested by calculations has been accepted as the solution of the problem. In this paper we seek a solution of the difficulty within the framework of a general formalism that starts from the spherical shell model and is capable of treating an arbitrary linear combination of multipole and pairing forces. With the restriction of the interaction to the familiar sum of a quadrupole multipole force and a monopole pairing force, we have previously studied a semi-microscopic version of the formalism whose framework is nevertheless more comprehensive than any previously applied to the problem. We obtained solutions for low-lying bands of several strongly deformed odd rare earth nuclei and found good agreement with experiment, except for an exaggerated staggering of levels for K=1/2 bands, which can be understood as a manifestation of the Coriolis attenuation problem. We argue that within the formalism utilized, the only way to improve the physics is to add interactions to the model Hamiltonian. We verify that by adding a magnetic dipole interaction of essentially fixed strength, we can fit the K=1/2 bands without destroying the agreement with other bands. In addition we show that our solution also fits 163Er, a classic test case of Coriolis attenuation that we had not previously studied.Comment: revtex, including 7 figures(postscript), submitted to Phys.Rev.

Perturbative study of multiphoton processes in the tunneling regime

A perturbative study of the Schr\"{o}dinger equation in a strong electromagnetic field with dipole approximation is accomplished in the Kramers-Henneberger frame. A prove that just odd harmonics appear in the spectrum for a linear polarized laser field is given, assuming that the atomic radius is much lesser than the free-electron quiver motion amplitude. Within this approximation a perturbation series is obtained in the Keldysh parameter giving a description of multiphoton processes in the tunneling regime. The theory is applied to the case of hydrogen-like atoms: The spectrum of higher order harmonics and the above-threshold ionization rate are derived. The ionization rate computed in this way determines the amplitudes of the harmonics. The wave function of the atom proves to be rigid with respect to the perturbation so that the effect of the laser field on the Coulomb potential in the computation of the probability amplitudes can be neglected as a first approximation: This approximation improves as the ratio between the amplitude of the quiver motion of the electron and the atom radius becomes larger. The semiclassical description currently adopted for harmonic generation is so rederived by solving perturbatively the Schr\"{o}dinger equation.Comment: Latex, 11 pages. To appear on Phys. Lett.

Time-varying Multi-regime Models Fitting by Genetic Algorithms

Many time series exhibit both nonlinearity and nonstationarity. Though both features have often been taken into account separately, few attempts have been proposed to model them simultaneously. We consider threshold models, and present a general model allowing for different regimes both in time and in levels, where regime transitions may happen according to self-exciting, or smoothly varying, or piecewise linear threshold modeling. Since fitting such a model involves the choice of a large number of structural parameters, we propose a procedure based on genetic algorithms, evaluating models by means of a generalized identification criterion. The performance of the proposed procedure is illustrated with a simulation study and applications to some real data.Nonlinear time series; Nonstationary time series; Threshold model