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.

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

An analysis of global warming in the Alpine region based on nonlinear nonstationary time series models

The annual temperatures recorded for the last two centuries in fifteen european stations around the Alps are analyzed. They show a global warming whose growth rate is not however constant in time. An analysis based on linear Arima models does not provide accurate results. Thus, we propose threshold nonlinear nonstationary models based on several regimes both in time and in levels. Such models fit all series satisfactorily, allow a closer description of the temperature changes evolution, and help to discover the essential differences in the behavior of the different stations

Time-varying multi-regime models fitting by genetic algorithms

Many time series exhibit both nonlinearity and non-stationarity. Though both features have been often taken into account separately, few attempts have been proposed for modelling 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 modelling. 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 non stationary model building by genetic algorithms

Many time series exhibits both nonlinearity and nonstationarity. Though both features have been often taken into account separately, few attempts have been proposed for modeling them simultaneously. We consider threshold models and present a general model allowing for several 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 proposed model building strategy is applied to a financial inde

Simulation and Use of Heuristics for Peripheral Economic Policy

Recent trends in Agent Computational Economics research, envelop a government agent in the model of the economy, whose decisions are based on learning algorithms. In this paper we try to evaluate the performance of simulated annealing in this context, by considering a model proposed earlier in the literature, which has modeled an artificial economy consisting of geographically dispersed companies modeled as agents, that try to maximize their profit, which is yielded by selling an homogeneous product in different cities, with different travel costs. The authors have used an evolutionary algorithm there, for modeling the agents' decision process. Our extension introduces a government agent that tries to affect supply and demand by different taxation coefficients in the different markets, in order to equate the quantities sold in each city. We have studied the situation that occurs when a simulated annealing algorithm and a simple search algorithm is used as the government's learning algorithm, and we have evaluated the comparative performance of the two.