A Computational Approach On Neighbourhood Structures In The Simulation Of Dichotomous Development

In this paper the issue of dichotomous growth and development is addressed by means of computer simulation. As previously remarked by many authors (see for example Marengo and Willinger [5], or McCain [6]), computer simulation is a key technique to model economic dynamics. The specific application of this study comes out from considerations related to the field of evolutionary economics. At the first corner of the ring we find the intuition of Kirman [2] which emphasises the importance of viewing to economy as an evolving network. In this context interaction is viewed as a leading aspect in modern economy, where individual behaviour arises as a synthesis of both previous personal experience and partnership effects. Although many different paths may be followed to approach this topic, this paper addresses to the specific field of simulations of interaction among individuals by means of spatial connections.In particular, we explore the emergence of dichotomous growth, when the spatial distribution is simulated through of connectivity structures well-known to topology representation theory and strictly related to the approach of self-organisation in neural models [3], [4]. The simulations have been performed starting from the two sector growth model suggested in McCain [6] with a few modification. As in McCain [6], we consider an overlapping generation system, where each individual lives for two periods. At each step the agent chooses how to allocate potential labour between work and study, and hence how to divide wages between consumption and savings which will be invested in physical capital to be used in the second part of his life. The production function for tangible goods is given by a Cobb-Douglas function: Q=(L K H)^1/3 Where, Q,L,K, and H are, respectively, production, labour services, tangible and human capital. New generations acquire from the old one previous situation with changes induced by learning and neighbourhood effects. Our efforts have been concentrated in the task of modelling such learning and neighbourhood effects. Our contribution stands primarily in the fact that in our model spatial connections affect not only the level of human capital available (and hence production), but also propensity to save as well as propensity to study. The following rules have been adopted: - at each step, two leaders (cell) of the process emerge as individuals who have shown, respectively, better rate of production and allocation of wages. Hence each cell will set its operative rules and modify previous strategy by taking into account emerging leaders of the step as well as spatial distance from them according to a smoothing function as the one below: f [ (i,j), l, csi,] = Exp[-csi d(l,(i,j))] where (ij) is the position of individual in the grid, l is the position of leader, csi is a positive constant arbitrarily chosen in (0,1), and finally d(l,(i,j)) is a proper metrics which computes the distance between the leader and the cell under examination.-The leaders in turn will change their previous rules by perturbing them by a random factor.The model is studied by adopting both a classical cross neighbourhood with various radius amplitudes and various clique typologies [1]. All the simulations have been implemented using Wolfram's Mathematica.