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

Multi-regime models for nonlinear nonstationary time series

Nonlinear nonstationary models for time series are considered, where the series is generated from an autoregressive equation whose coe±cients change both according to time and the delayed values of the series itself, switching between several regimes. The transition from one regime to the next one may be discontinuous (self-exciting threshold model), smooth (smooth transition model) or continuous linear (piecewise linear threshold model). A genetic algorithm for identifying and estimating such models is proposed, and its behavior is evaluated through a simulation study and application to temperature data and a financial index.

Kerman-Klein-Donau-Frauendorf model for odd-odd nuclei: formal theory

The Kerman-Klein-Donau-Frauendorf (KKDF) model is a linearized version of the Kerman-Klein (equations of motion) formulation of the nuclear many-body problem. In practice, it is a generalization of the standard core-particle coupling model that, like the latter, provides a description of the spectroscopy of odd nuclei in terms of the properties of neighboring even nuclei and of single-particle properties, that are the input parameters of the model. A divers sample of recent applications attest to the usefulness of the model. In this paper, we first present a concise general review of the fundamental equations and properties of the KKDF model. We then derive a corresponding formalism for odd-odd nuclei that relates their properties to those of four neighboring even nuclei, all of which enter if one is to include both multipole and pairing forces. We treat these equations in two ways. In the first we make essential use of the solutions of the neighboring odd nucleus problem, as obtained by the KKDF method. In the second, we relate the properties of the odd-odd nuclei directly to those of the even nuclei. For both choices, we derive equations of motion, normalization conditions, and an expression for transition amplitudes. We also solve the problem of choosing the subspace of physical solutions that arises in an equations of motion approach that includes pairing interactions.Comment: 27 pages, Late

Application of the Kerman-Klein method to the solution of a spherical shell model for a deformed rare-earth nucleus

Core-particle coupling models are made viable by assuming that core properties such as matrix elements of multipole and pairing operators and excitation spectra are known independently. From the completeness relation, it is seen, however, that these quantities are themselves algebraic functions of the calculated core-particle amplitudes. For the deformed rare-earth nucleus 158Gd, we find that these sum rules are well-satisfied for the ground state band, implying that we have found a self-consistent solution of the non-linear Kerman-Klein equations.Comment: revtex and postscript, including 1 figure(postscript), submitted to Phys.Rev.Let

Coevolutionary Genetic Algorithms for Establishing Nash Equilibrium in Symmetric Cournot Games

We use co-evolutionary genetic algorithms to model the players' learning process in several Cournot models, and evaluate them in terms of their convergence to the Nash Equilibrium. The "social-learning" versions of the two co-evolutionary algorithms we introduce, establish Nash Equilibrium in those models, in contrast to the "individual learning" versions which, as we see here, do not imply the convergence of the players' strategies to the Nash outcome. When players use "canonical co-evolutionary genetic algorithms" as learning algorithms, the process of the game is an ergodic Markov Chain, and therefore we analyze simulation results using both the relevant methodology and more general statistical tests, to find that in the "social" case, states leading to NE play are highly frequent at the stationary distribution of the chain, in contrast to the "individual learning" case, when NE is not reached at all in our simulations; to find that the expected Hamming distance of the states at the limiting distribution from the "NE state" is significantly smaller in the "social" than in the "individual learning case"; to estimate the expected time that the "social" algorithms need to get to the "NE state" and verify their robustness and finally to show that a large fraction of the games played are indeed at the Nash Equilibrium.Comment: 18 pages, 4 figure

Stabilization with arbitrary laser polarizations

Published versio

Intense field stabilization in circular polarization: 3D time-dependent dynamics

We investigate the stabilization of a hydrogen atom in circularly polarized laser fields. We use a time-dependent, fully three dimensional approach to study the quantum dynamics of the hydrogen atom subject to high intensity, short wavelength laser pulses. We find enhanced survival probability as the field is increased under fixed envelope conditions. We also confirm wavepacket dynamics seen in prior time-dependent computations restricted to two dimensions.Comment: 4 pages, 3 figures, submitte

Foundations of self-consistent particle-rotor models and of self-consistent cranking models

The Kerman-Klein formulation of the equations of motion for a nuclear shell model and its associated variational principle are reviewed briefly. It is then applied to the derivation of the self-consistent particle-rotor model and of the self-consistent cranking model, for both axially symmetric and triaxial nuclei. Two derivations of the particle-rotor model are given. One of these is of a form that lends itself to an expansion of the result in powers of the ratio of single-particle angular momentum to collective angular momentum, that is essentual to reach the cranking limit. The derivation also requires a distinct, angular-momentum violating, step. The structure of the result implies the possibility of tilted-axis cranking for the axial case and full three-dimensional cranking for the triaxial one. The final equations remain number conserving. In an appendix, the Kerman-Klein method is developed in more detail, and the outlines of several algorithms for obtaining solutions of the associated non-linear formalism are suggested.Comment: 29 page

Semiclassical description of multiphoton processes

We analyze strong field atomic dynamics semiclassically, based on a full time-dependent description with the Hermann-Kluk propagator. From the properties of the exact classical trajectories, in particular the accumulation of action in time, the prominent features of above threshold ionization (ATI) and higher harmonic generation (HHG) are proven to be interference phenomena. They are reproduced quantitatively in the semiclassical approximation. Moreover, the behavior of the action of the classical trajectories supports the so called strong field approximation which has been devised and postulated for strong field dynamics.Comment: 10 pages, 11 figure