The Model of Socio-Economic Stratification of Society Based on An Agent Approach, Taking Into Account Rank Exchange
Authors: Kapitanov V. A. , Osipova O. S. , Maksimova A. U. 
Published: March 2023

The purpose of the study is to demonstrate the possibility of adequate mathematical modeling of property inequality in a stratified society based on an agent approach, taking into account the unequal (rank) exchange between agents with different socio-economic status. To achieve this goal, it was necessary to solve the following tasks:1. To develop minimum criteria for the adequacy of mathematical models of socio-economic inequality.2. To substantiate the advantages of mathematical models based on an agent approach using rank exchange.3. To present the author’s version of the mathematical model of the goods’ movement in society based on an agent approach, taking into account rank exchange.4. To check the author’s mathematical model for compliance with the minimum qualitative criteria of adequacy and to create a quantitatively coinciding with the real distribution of the country’s population of the Russian Federation by income.5. Determine the limitations of the developed mathematical model by the authors.Materials and methods. The paper used statistical data from Rosstat, the Federal Tax Service of the Russian Federation, the World Bank, the US Bureau of the Census, the Edelman Trust Barometer, as well as data published by domestic and foreign researchers of inequality. These data were compared with the results of inequality calculations obtained using the mathematical model of the goods’ movement in society based on an agent approach, taking into account rank (nonequivalent) exchange.Results. The minimum criteria that any adequate model of stratification of society must meet are defined: 1. reveals a lognormal distribution of the population by income with a heavy tail; 2. reflects in long-term historical retrospect the trend of inequality growth; 3. demonstrates a short-term reduction of inequality during periods of socio-economic crises.The proposed model meets these requirements, it demonstrates not only qualitative, but also quantitative adequacy – reproduces by calculation the curve of the actual distribution of Russian society by income.Common concepts of inequality, in particular, the theory of superstars or skill-based technological change do not allow achieving such a result. The limitations of the created mathematical model are shown:– the impossibility of creating an adequate Lorentz curve with insufficient computing power;– inability to describe changes in cross-country inequality, since countries are not subjects of rank exchange, although interstate agreements certainly have an impact on the exchange between economic subjects of social interaction;– inability to describe situations of absolute poverty, i.e. long-term decline in income, although in the real economy such situations are sometimes observed;– the endless growth of inequality over time, whereas in reality economic processes of inequality growth are always opposed by social processes of counteraction to this growth.Conclusion. The mechanism of spontaneous emergence and growth of income (property) inequality as an inevitable consequence of market relations is demonstrated.The agent-based approach, taking into account the rank exchange, can allow identifying critical moments in time, after which extraordinary economic and socio-political consequences will have an irreversible character, and can also help in studying the influence of individual behavior of economic agents of different levels on the evolution of the entire economic, and as a consequence, socio-political system.The results obtained will be useful for strategic planning, when developing target indexes for the socio-economic development of regions and the country as a whole, and improving the methodology for calculating key performance indexes for civil servants