(1)where Xij(t) is the state of the ij-cell that contains resource particle at the time t,
Summary. Original technique of economic agents competitive strategies identification based on empirical data is proposed. Instead of traditional qualitative verbal description of strategies and comparison of firms with different kinds of animals (foxes, lions, etc.) the quantitative triangle diagram is used that looks like the three-component phase diagram. Agents’ positions inside this triangle are determined by two dynamic empirical parameters. Corresponding points discover the superposition of three main competitive strategies (ruderals, stress-tolerants, competitors) in agent’s behavior.
The technique proposed is used for identification of competitive strategies of banks at the Russian financial market. Analysis is carried out for 32 credit institutions. Computer simulation and pattern recognition techniques were used in order to obtain some features of proposed empirical strategies identification.
Key words. Strategies identification, competition simulation, bank system.
An adequate reaction by economic agents to the changing external conditions (both fluctuations and trends) makes the essence of their competitive strategy.
There are no precise quantitative characteristics of strategies in economic analysis; the strategy proposed by the headquarters very often differ with the real firm behavior. Similarity between animals and firms competition helps to understand behavior of economic agents. Economic agents strategies are described in a qualitative verbal form: companies are compared with different kinds of animals – foxes, lions etc. (Yudanov, 1990). The most enhanced application to competitive strategies identification was done in plant sciences (Grime, 1979).
The goal of the present study is development of a technique for identification of the economic agent’s competitive strategy based on empirical data. This technique can be compared with the well-known classification methods (pattern recognition).
When studying countries with transitive economies it would be most conveniently to use the data of dynamically progressing markets, appeared as a result of economic transformations. These demands are complied by the banking sector of economy, developing in Russia during the last decade.
Disproportion in credit and financial system since 1988 brought to formation of powerful misbalance in the structure of economy (for example, the regional irregularity of assets, where 15 largest Moscow banks own 29 %, while the regional banks - only 16%). It resulted in active redistribution of resources among credit institutions during the last decade, followed by large-scale fluctuations. The situation arisen is unique for it allows to observe considerable structural changes in the banking sector of economy, occurring naturally within a short period of time.
Russian bank system has passed five main stages (Evseev, 1997). The last one (August, 1998 – 2001) is a period of crisis and restructuring: the number of banks decreased from 2500 (1995) to 1300 (the end of 2000). It is the most informative period for our study for the crash of 1998, resulted in bankruptcy of banks and redistribution of their client base owing to competition took place.
For the analysis of banks’ evolution we used data for the beginning of every month during the period since January of 1999 to January of 2000. Thus, the period analyzed covered one calendar year. Statistical data source were the bank balances of secondary order accounts of thirty two credit institutions (Appendix 1). They were selected in such a way that both small and medium regional and Moscow banks, and largest federal ones were included; this made the selection more representative.
The strategy in present study means the agents behavior and its response to the changing external conditions (Mintzberg, Ahlstrand, Lampel 1998): a bank’s capacity for overcoming stresses, rehabilitating itself after crises (disturbances), compete for a resource.
According to the ecological strategies approach in plant sciences (Grime, 1979) a stress is determined as lack of resources for growth and development, disturbance – as damage of an object either resulting in its death or considerably hindering its growth, while competition is determined as aspiration of neighboring objects for using the same resources.
In correspondence with the mentioned above three leading factors of the life struggle there are singled out three types of primary strategies optimal under predominance of each given factor: i) competitors (C), striving for efficient use of resources through reduction of prime and production costs; ii) stress-tolerants (S), aiming to avoid competition through creation of a unique niche which is inaccessible for others; iii) ruderals (R), aspiring for profit maximization under conditions of few competitors and considerable volume of resources, efficiency of resource utilization being less important.
As a rule, objects with precisely expressed primary strategies do not exist. In reality there take place the so called secondary strategies – superposition of the primary ones. To identify the intermediate types of strategies in plant sciences there was developed a classification diagram.
An agent uses its biotic potential to survive in struggle for life. Its survival in certain conditions depends on which part of its potential it would use to overcome each of mentioned above unfavourable factors. Quantitatively the value of its efforts can be shown with numerical value of corresponding indices: Ic – overcoming of competition; Is – of stress; Id – of disturbance. It is obvious that only two indices are independent variables for the sum of these indices’ values – the agent’s potential – is constant. Values of all three indices are sidetracked on the plane triangular diagram, similar to the phase diagram of the three-component system, fig. 1. Objects with primary strategies (R, S, C) are arranged in angles. Secondary strategies correspond to the points inside the triangle.
Competitors-ruderals (CR) adapt to places of inhabitance where low stress and competition are limited with average intensive disturbance. Ruderals-stress-tolerants (RS) adapt to non-productive places of inhabitance not disturbed much. Competitors-stress-tolerants (CS) adapted to relatively not disturbed places with average intensive stresses. Competitors-stress-tolerants-ruderals (CSR) adapt to the conditions when the competition level is limited with the middle level of stress and disturbance intensity (Grime, 1979).
Identification of an agent’s competitive strategy requires the numerical parameters characterizing the agent’s opposition to each type of unfavourable conditions (two is enough). These parameters can differ for various systems. A simulation model has been used to find out what parameters are required.
The limited resource is the subject of competition in the “game with the zero sum” multi-agent models (Giblons, 1992). Such resource in financial market is money.
Earlier the authors have proposed a new model of agents growth and competition: traditional “game with the zero sum” is extended with consideration of agents environment (Berg, 2000; Berg and Popkov, 2001). Growth and competition are performed by resource assimilation and dissimilation based on reversible diffusion-limited aggregation rule (Witten, Sander, 1983).
Agents growth and competition model is performed on the square lattice (average size is about 5000x5000) that represents the restricted economic space with periodic boundary conditions (lattice is closed in torus). Limited resource is presented by the particles migrating (L) from one cell to another according to brownian motion rules by Margolus (Toffoli and Margolus, 1990) that may be assimilated by the agent and become immovable (S). Agents are presented by single cells (A) that are the "aggregation" centers for resource particles L. Assimilation of resource L by the agent A is performed according to diffusion-limited aggregation (DLA) algorithm (resource assimilation rule)
(1)
where Xij(t) is the state of the ij-cell that contains resource
particle at the time t,
Mij(t) = {Xi+1,j(t); Xi-1,j(t); Xi,j+1(t); Xi,j-1(t)} is the vicinity of ij-cell.
The rule (1) means that when the migrating resource particle (L) at the time t comes closely to the agent (A) or resource assimilated (S) by this agent it is also assimilated by this agent at the time t+1. Lattice cells occupied by the assimilated particles form clusters with fractal shape.
In order to satisfy the agents competition and environment stress that result in dissimilation of resource assimilated by the agent earlier the well-known irreversible DLA mechanism (1) was extended by the following reversible rule (resource dissimilatiom rule)
(2)
where k is coordination number of S particle in ij-cell
{S Ç Mij(t)}, k=1..4. The proposed reversibility
makes possible to separate an earlier aggregated cluster surface particle under
the probability Pk.
The total amount of resource (the sum of L and S particles) at the lattice is constant. Initially only L particles exist and are distributed at random (with concentration Co ). A certain number of agents (1 or more) also exist initially. Each agent is characterized by its own values of Pk parameters. During the growth process other agents may appear at the lattice as well as the Pk parameters shift may take place for one or more agents according to the study goal.
There was studied single agent growth with different Pk values in the environment with the variety of resource amount (Co).
Co value reflects the stress: the lower Co corresponds to the higher stress level. It was obtained that the low values of resource concentration Co led to decrease of agent growth velocity.
Pk are the individual agent’s parameters determining resource assimilation/dissimilation – i.e. the agent’s competition strategy behavior. Agent growth velocity decreases for the higher values of Pk. Artificial agent (cluster) becomes more compact, its density increases.
Variety of Pk values during the agent growth process makes it possible to study the agent’s behavior under the shift of environmental conditions. Step shifts of Pk parameters from low to high values for one and the same agent during the period of its living in artificial economic system plays the role of evolutionary inflation (Mayevsky, Kazdan, 1998). Evolutionary inflation is the result of innovations when a “new” agent (innovator) is able to pay more for one and the same amount of resource than “old” ones. By this way the “new” agent is more successful in competition for resource. Appearance of such more and more successful agents-innovators means step-by-step increase of Pk for the “old” agent.
Disturbance is simulated as high amplitude fluctuations of Co (decrease) or Pk (increase) for a short period of time.
There can be observed three types of agents’ shapes: fractal; non-fractal (high density) compact cluster; compact cluster, disintegrated to subclusters. Certain combinations of Co and Pk lead to full dissimilation of an agent (cluster).
During the agent’s life cycle its shape is changing from one type to another due to the evolutionary inflation (step-by-step increase of Pk). The cycle is over when the agent is dissimilated, fig. 1.
Agent’s evolution (birth, growth, death) like the behavior of nonlinear dynamic system may be described in phase space in coordinates “M-M’”, where M is the total amount of resource, assimilated by agent by the moment of time t, M’=dM/dt. M and M’ parameters reflect the Ic and Is indexes respectively. So the phase diagram may be drawn in triangle shape, fig. 1.
According to results of artificial competition study the bank’s assets were taken as the index of competition and its growth rate – as the stress index. There are observed the following types of competitive strategies, fig 2a.
A group of “super-competitors” (marked out with triangles). They have near monopolistic access to resources owned by the state or certain industry branch served by them (mainly, the source industry - gas and oil producing industry, etc.).
Competitive “stress-tolerants” (marked out with circles). They do not possess monopolistic access to resources, therefore compete with each other on the common basis. These banks during 8-10 years of work on the market adapt themselves for the main stress – constant lack of resources.
Fig. 1. Diagram for localization of agents with different competitive strategies.
Values of indexes characterize agents’ overcoming of competition (Ic),
stress (Is) and disturbance (Id) in arbitrary units. Primary
strategies: C – competitors; S – stress-tolerants; R –
ruderals; C-S; C-R; S-R, C-S-R – areas of secondary strategies.
1, 2, 3 – points of economic agent’s life cycle (computer simulation). For shapes of “agent-cluster” see insertions. The total amount M of resource assimilated by the agent (cluster mass) corresponds to Ic; M’=dM/dt corresponds to -Is.
Fig. 2 a,b. Identification of banks strategies at the Russian financial market
(1999 – 2000). M – bank’s assets for 1999.01.01 (Russian rubles), M’=(1/M)·
dM/dt – normalized increase of assets per month (in %) averaged for 12 months.
Axes are marked in logarithmic scale.
a – all the banks listed in Appendix 1. Banks with C and C-R strategies are marked by triangles, S – by squares, S-C – by circles. Thin lines towards one of the circles show the corresponding M and M’ values.
b – banks with S-C strategy. Behavior of numbered banks is discussed in the text.
Typical “stress-tolerants” (marked out with squares) determine their main strategy not in seizing major part of the market but saving their own niche through serving companies-owners and/or their prominent partners.
The more detailed analysis of the second group (fig. 2b) shows that there are banks inside the group (1, 2), sticking (with respect to others) to the ruderal strategy. These are speculative banks dealing with high risks in exchange for high profits on a quickly growing market.
A separately standing bank (3) had, in fact, no assets growth, which reflected its serious internal problems. By the end of the year of 2000 its position became critical.
Banks 4 and 5, being former specialized banks, had a rather stable clientele. Under conditions of economic transformations these clients could not achieve high economic showings. Therefore the mentioned banks occupying their own niches operated in conditions of constant shortage of resources. They acted carefully even despite the quickly growing market.
Other banks shown at the fig. 2b kept to one and the same strategy, which (with respect to others) could be called competitive. Indeed, banks of this group operating in the same region met a severe competition.
Thus, it becomes obvious that economic conditions for Russian banks differ so much that they use various effective strategies: banks actually occupy different resource niches (resource base of Russian commercial banks is formed by the natural monopolies, town-forming enterprises and other big industrial companies, as well as small business and individuals).
Banks at the internal Russian financial market basically consider disturbance and stress to be institutional limitations determined by the state.
Evolutionary changes can be revealed by mathematical methods of classification (pattern recognition) of dynamically changing indices. The idea of pattern recognition methods lies in search of the best statistical decision function, allowing to divide k of elements from a test sampling on the basis of a beforehand known division of training selection from m of elements on n of given classes (Theodoridis, Koutroumbas 1998).
Formation of a training sample was based on the cluster analysis (recognition without training) of data for January 1, 1999 (m=32) with use of most informative indications: volume of assets, sufficiency of capital, liquidity, profitability. The mentioned informative indications are numerically characterized with currency of balanced trade, capital sufficiency factor, instantaneous liquidity factor (standard N2 of Russian Central Bank Regulations No1), efficiency factor correspondingly. Methods of calculating the mentioned indices are explicitly described in the work (Parishev, Frolov,1999). Besides, the mentioned informative indications were selected from a much broader initial set of aggregated parameters, including the structure and quality of bank’s assets and liabilities. In all, there were distinguished n=5 of classes. Banks within every class were similar in volume and specificity of operations. Large banks of federal level refer to the first class, small regional ones – to the fifth.
The classification task was most accurately solved with the method of potential functions (Appendix 2). With use of data for March 1, 1999 as a test sample (k=32) the quality of classification made 94%, a rather high result, which corroborates validity of dividing the investigated selection of banks on the given number of classes. Such classification reflects the banks resource base.
Evolution changes of banks parameters may result in shift of bank from initial class to another one. Three types of behavior during 1999-2000 were observed: i) preservation of initial position in the class, ii) transition to a higher class, iii) recurrent transitions between two adjacent classes.
The first type reflects relative stability of the bank in the market.
The second type is the result of growth of a bank’s share in the market due to redistribution of clientele of the banks not available to carry out their own obligations.
The third type can be a consequence of certain relativity in determining class boundaries. Transitions of such type can also be explained by the fact that a bank without a widely diversified client base directly depends either on some enterprise or a group of enterprises with volume of financial flows having certain structure and periodicity. Thus, interchange of certain “downfalls” and “up-flights” could fall on report dates.
The forth type (not observed among the analyzed banks): transition of a bank to a lower class due to the loss by this very credit institution of a certain share in the market of bank services and general deterioration of its financial state.
Thus, transition of banks between classes reflects the real redistribution of resource base.
Results of empirical analysis visually show that within the period since January of 1999 to January of 2000 there takes place an active evolutionary process, affected seventeen banks of thirty two under research.. Most of them are characterized with extension of their resource base. High intensity of this process is connected with redistribution of corporate and individual clients after the crisis of August, 1998.
There is no doubt that bank classification (pattern recognition) could be made in space of the same indications used while constructing the competitive diagram. However, the bank’s positioning on the diagram gives us new information about the type of its competitive strategy and status with respect to other banks, reflecting functional peculiarities of both the very bank and its competitors. The results of such functional positioning would allow to make adequate administrative decisions. They are of great importance for administration of the bank itself to elaborate an optimum strategy in a concrete situation, and for persons making state policy in the banking sector – to create conditions for banks, most completely meeting the task of economic evolution.
At present time Russian banking society realizes the necessity to develop a multilevel national banking system, which requires saving of existing resource niches and creating of new ones. This research proves that for successful banks development for every such resource niche there should be established individual institutional limitations - flexible regulation system for the banks due to their functional types.
Results of the present study were used in preparation of “The Base Concept of Russian bank system development" that was approved at the X Congress of Association of Russian Banks (May 2000, Moscow).
The research has been carried out under partial financial support of Russian Humanitarian Scientific Fund, grant No 01-02-00114a.
AvtoBank (Moscow), Alpha-Bank (Moscow), AKB “BIN” (Moscow), VUZ-Bank (Ekaterinburg), Vyborg-Bank (Vyborg), Grancombank (Ekaterinburg), KB “Guta-Bank” (Moscow), Dalnevostochny Bank (Vladivostok), KB “Dialog-Optim” (Moscow), Zapsibcombank (Tumen), Gold-Platinum-Bank (Ekaterinburg), KB “Infobank” (Moscow), AKB “MDM-Bank” (Moscow), Mezhtopenergobank (Moscow), AKB “Metallinvestbank” (Moscow), MKB “Moskomprivatbank” (Moscow), KB “Pavaletsky” (Moscow), KB “Petrovsky” (S.-Petersburg), AKB “Probiznesbank” (Moscow), AKB “Promradtekhbank” (Moscow), Promstroybank (S.-Petersburg), AKB “Rosbank” (Moscow), AKB “Russlavbank” (Moscow), Sverdlsotsbank (Ekateriburg), Bank “Severnaya Kazna” (Ekaterinburg), Spetsinvestbank (Moscow), Urals Bank of Reconstruction and development (Ekaterinburg), Uralvneshtorgbank (Ekaterinburg), Uralpromstroybank (Ekaterinburg), Urals-Siberian bank for Social development (Ekaterinburg), Uraltransbank (Ekaterinburg).
All data are from the Uralvneshtorgbank database.
2. Construction of a decision rule by potential functions technique
The training sample consists of 32 objects 
,
, divided into 5 classes 
,
. It is required to find a decision
function, which would give the best recognition percent for the control sample
from 
objects.
The solution was found by method of potential functions extension-contraction.
Potential functions 
– decreasing functions
from a distance x to a certain point. For each vector x of the
received for recognition massif from k vectors there are calculated functions
where the distance 
, 
- adjusting factors, providing necessary “extension-contraction” of potential
functions. The vector is considered the element of that class whose function
takes the maximum value.