The dynamical behavior of ensembles of autonomous systems as applied to large scale systems behaviour of economic and societal systems

Abstract

The purpose of this paper is to present a reformulation of the classical control system optimization problem to incorporate the interrelationships of autonomous subsystems which are ordinarily found in the systems description of economic and social systems. Autonomy exists in such descriptions because we recognize that what is being modelled is a population of quasi-independent entities (agents) which each have their own objective function. Much work has been done in analyzing the dynamics of large-scale systems, in terms of hierarchial interrelationships among them and direct control actions of a ‘master’ unit. Recent work has found that economic systems can be modelled more accurately by recognizing that global behaviors are a superposition of behaviors among a set of competing/cooperating subsystems which obey two basic conservation laws regarding the wealth function which completely describes the agent's state. Further, economic systems can be shown to be far from equilibrium because of autocatalytic subsystems. Populations are not static nor returns to capital always zero. In short, the Malthusian and Marxian paradoxes drive economic systems of all types and lead to increasing complexity which is incorporated into the mathematical models explicitly. Simulation studies also have given us some specific findings regarding the spontaneous development of cooperative behaviors among autonomous units. These are congruent with behaviors derived from analysis of a system's price function stability when making the wealth function an extremum. It is therefore proposed that classical systems modelling has failed to handle systems which have the properties described in this paper and that such systems in fact are the type in which socio-economic/ecological problems are embedded. In particular, a revised analog of the Second Law, that the number of states required to describe an ensemble of autonomous systems must increase monotonically over time is derived. Again, recent empirical evidence has substantiated this result.