Economic agents (EAs) evolution model is based on the physical growth process. Restricted economic space is presented by square lattice up to 5000*5000 cells. Resource particles are migrating between the lattice cells according to brownian motion rules. EAs are the "aggregation" centers for resource particles. Interaction between EAs clusters and resource particles is performed according to diffusion-limited aggregation (DLA) algorithm. A well-known irreversible DLA mechanism is enhanced by reversible rule in order to satisfy the EAs competition environment. The proposed reversibility makes it possible to separate an earlier aggregated cluster surface particle under the probability Pk, where k is the particle coordination number. (Reversible DLA together with irreversible DLA and RLA mechanism presents the complete description of aggregation process in colloidal systems. Reversible aggregation takes place in a secondary minimum of colloid particles pair interaction potential). Proposed model is designed in "cell automata" media.
The goal of the present paper is to obtain the number of prognostic scenarios of agents growth and corresponding market evolution under the agents competitions for limited resource. The whole study is focused at the EAs grows kinetics, structure parameters and their dependence on growth conditions on the markets with equal and non-equal competition.
Parameters of the proposed model are in relationship with characteristics of competition in the bank sector of Russian financial market. Under the equal competition EAs grows is determined mainly by the positive feedback. Under the non-equal competition two scenarios of EAs evolution are obtained: (i) stable growth; (ii) degradation. In transition regime from (i) to (ii) the role of fluctuations increase. In (ii) case the multiagent market transforms to monopolistic one. The problems of EAs stability to crisis stress in (i) and(ii) scenarios is also discussed. According to self-organization critically theory the crisis stress is supposed to be the result of "avalanche" of certain amplitude and longitude. It was observed that the winner of non-equal competition may have the less stable structure than the looser one. It was found that agent tolerance to crisis stress may be increased by specific artificial procedure - a number of crises with small amplitude each - it looks like the "vaccination". Dependence of "vaccination" intensity and agent crisis-resistance is estimated. At the same time such a procedure will provide market transition from one metastable state to another with minimum loss.
Results of present study were used in proposals for development of Russian bank system (Bank and Technologies, 2000, ¹1, p.78-85)