A discreet ‘power-society-economics’ model based on cellular automaton

In this paper we consider a new modification of the discrete version of Mikhailov's ‘power-society’ model, previously proposed by the author. This modification includes social-economical dynamics and corruption of the system similarly to continuous ‘power-society-economics-corruption’ model but is based on a stochastic cellular automaton describing the dynamics of power distribution in a hierarchy. This new version is founded on previously proposed ‘power-society’ system modeling cellular automaton, its cell state space enriched with variables corresponding to population, economic production, production assets volume and corruption level. The social-economical structure of the model is inherited from Solow and deterministic continuous ‘power-society-economics-corruption’ models. At the same time the new model is flexible, allowing to consider regional differentiation in all social and economical dynamics parameters, to use various production and demography models and to account for goods transit between the regions. A simulation system was built, including three power hierarchy levels, five regions and 100 municipalities, and a number of numerical experiments were carried out. This research yielded results showing specific changes of the dynamics in power distribution in hierarchy when corruption level increases. While corruption is zero (similar to the previous version of the model) the power distribution in hierarchy asymptotically tends to one of stationary states. If the corruption level increases substantially, volume of power in the system is subjected to irregular oscillations, and only much later tends to a stationary value. The meaning of these results can be interpreted as the fact that the stability of power hierarchy decreases when corruption level goes up.