The Model of Socio-Economic Stratification of Society Based on An Agent Approach, Taking Into Account Rank Exchange

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

1. Blok M. Koroli-chudotvortsy: Ocherk predstavleniy o sverkh”yestestvennom kharaktere korolevskoy vlasti, rasprostranonnykh preimushchestvenno vo Frantsii i v Anglii = Miracle-Working Kings: An Essay on the Ideas of the Supernatural Character of Royal Power, Prevalent Predominantly in France and England. Moscow: Language of Russian culture; 1998. 709 p. (In Russ.)

2. Rosen S. The Economics of Superstars. American Economic Review. 1981; 71; 5: 846.

3. Goldin S., Katz L.F. The Race between Education and Technology. Harvard: Harvard University Press, 2008.

4. Kapelyushnikov R.I. Neravenstvo: kak ne primitivizirovat’ problemu (kriticheskiye zametki) = Inequality: how not to primitivize the problem (critical notes). Moscow: Publishing House of the Higher School of Economics, 2016. (Series WP3 “Problems of the labor market”). 40 p. (In Russ.)

5. Kuznets S. Economic growth and income inequality. The American Economic Review. 1955; 45; 1: 1-28.

6. Marks K. Kapital: kritika politicheskoy ekonomii = Capital: criticism of political economy. Moscow: Eksmo; 2017; 1; 1200 p. (In Russ.)

7. Kapitanov V.A., Maksimova A.YU, Osipova O.S. Improving the system of social management and forecasting by eliminating a number of statistical collisions. EKONOMIKA. NALOGI. PRAVO = ECONOMY. TAXES. RIGHT. 2020; 1: 72-86. (In Russ.)

8. Kapitanov V.A., Ivanova A.A., Maksimova A.Yu. Advantages of the distribution function as a method of graphic representation of the economic structure of society. Statistika i ekonomika = Statistics and Economics. 2018; 15; 1: 4-16. (In Russ.)

9. Piketti T. Kapital v XXI veke = Capital in the XXI century. Moscow: Ad marginem; 2015. (In Russ.)

10. Zhou Y, Song L. Income inequality in China: causes and policy responses. China Economic Journal. 2016; 9; 2: 186-187.

11. Tikhonova N.Ye., Lezhnina Yu.P., Mareyeva S.V., Anikin V.A., Karavay A.V., Slobodenyuk Ye.D. Model’ dokhodnoy stratifikatsii rossiyskogo obshchestva: dinamika, faktory, mezhstranovyye sravneniya = Model of income stratification of Russian society: dynamics, factors, cross-country comparisons. Moscow; Saint Petersburg: Nestor-Istoriya; 2018. 368 p. DOI: 10.317544469-1419-7. (In Russ.)

12. Kapitanov V.A., Ivanova A.A., Maksimova A.YU. Problems of numerical estimates of inequality. Statistika i ekonomika = Statistics and Economics. 2018; 15(4): 4-15. DOI: 10.21686/2500-3925-2018-4-4-15. (In Russ.)

13. Van Zanden YA.L. Where is the beginning of the Kuznets curve? Western Europe in the Early Modern Period. (translated from English by N.V. Buturlina). Economic history. Yearbook. 2004. Moscow: Russian Political Encyclopedia (ROSSPEN); 2004. 598 p. (In Russ.)

14. Wooldridge M. Agent-based computing. Interoperable Communication Networks 1998; 1: 71-98.

15. Drăgulescu A, Yakovenko V. M. Statistical mechanics of money. Department of Physics [Internet]. USA: University of Maryland, College Park, MD 20742-4111. Available from: https:// arxiv.org/pdf/cond-mat/0001432.pdf.

16. Lo Cascio E., Malanima P. GDP in Pre-Modern Agrarian Economies (1-1820 AD). A Revision of the Estimates. Rivista di Storia Economica [Internet]. 2009. XXV. Available from: http://www.paolomalanima.it/default_file/Papers/GDP_in_Pre-Modern_Agrarian_Economies.pdf.

17. Greber D. Dolg: pervyye 5000 let istorii = Debt: the first 5000 years of history. Moscow: Ad Marginem Press; 2015. (In Russ.)

18. Mommzen T. Istoriya Rima = History of Rome. Rostov on Don: Phoenix; 1997. 640 p. (In Russ.)

19. Osipova O. S. Upravleniye ustoychivym razvitiyem = Management of sustainable development. Saint Petersburg: LLC Publishing house Real economy; 2015. 473 p. (In Russ.)

20. Romanov V., Yakovlev D., Lelchuk A. Wealth distribution evolution in an agent-based computational economy. Lecture Notes in Economics and Mathematical Systems, Publisher: Springer Berlin Heidelberg. 2010. 645 p. DOI: 10.1007/978-3-642-13947-5_16. Available from: https://www.anylogic.ru/upload/iblock/217/217368b3fa2733458e-d439a8ebbea8d.pdf. (In Russ.)

21. Gidulyanov V. The formula of the “civilized market”. Institut mikroekonomiki minekonomiki RF, «Pravila igry» = Institute of Microeconomics of the Ministry of Economy of the Russian Federation, “Rules of the Game”. 1998; 4: 22-29. (In Russ.)

22. Hunter A. V., Nutaro J.J., Kalyan S. P. An agent-based model of the observed distribution of wealth in the United States [Internet]. Journal of Economic Interaction and Coordination. 2018; 13: 641–656. Available from: https://link.springer.com/article/10.1007/s11403-017-0200-9.

23. Kapelyushnikov R. I. Neravenstvo – vselenskoye zlo?= Inequality - a universal evil? Moscow: Ed. House of the Higher School of Economics; 2019. 28 p. (Series WP3 “Labor Market Issues”). (In Russ.)

24. Krapivsky P.L., Redner S. Wealth distributions in asset exchange models [Internet]. The European Physical Journal B - Condensed Matter and Complex Systems. 1998; 2: 267–276. Available from: https://arxiv.org/abs/1006.4595v1.

25. Kapitanov V.A., Ivanova A.A. Influence of the proportional distribution of the total surplus on the property stratification [Internet]. Ekonomika i Prognozirovaniye. Kiyev = Economics and Forecasting. Kyiv. 2014; 3: 125–136. Available from: http://eip.org.ua/docs/EP_14_2_125_ru.pdf.

26. Maddison A. Contours of the world economy, 1-2030 AD. Essays in macro-economic history. Oxford: Oxford University Press; 2007.

27. Tremblay S. The daily costs of living like a billionaire [Internet]. 2021. Available from: https://www.gobankingrates.com/money/wealth/daily-costs-living-like-billionaire.

28. Kapitanov V.A., Ivanova A.A. Criticism of the economic foundations of nationalism. Statistika i ekonomika = Statistics and Economics. 2017; 14; 4: 4-13. (In Russ.)

29. Myurdal’ G. Sovremennyye problemy “tret’yego mira” = Modern problems of the “third world”. Moscow: Progress; 1972. 768 p. (In Russ.)

30. Raynert E. Kak bogatyye strany stali bogatymi, i pochemu bednyye strany ostayutsya bednymi = How rich countries got rich and why poor countries stay poor. Moscow: House of the Higher School of Economics; 2011. 384 p. (In Russ.)

31. Kapitanov V.A., Ivanova A.A., Maksimova A.YU. Identification of trends in the decline in incomes of the US population over the past five decades. Statistika i ekonomika = Statistics and Economics. 2019; 16; 5: 94-110. DOI: 10.21686/2500-3925-2019-5-94-110. (In Russ.)

32. Osipova O.S., Kapitanov V.A. The dynamics of social inequality in the digital economy: a look from the past into the future [Internet]. Ekonomika. Nalogi. Pravo = Economics. Taxes. Right. 2018; 11; 2: 27-41. Available from: http://www.fa.ru/org/div/edition/enp/journals/2018%20№2.pdf. (In Russ.)

33. Carlos Newland. Is support for capitalism declining around the world? A free-market mentality index, 1990–2012. The Independent Review [Internet]. Journal of political economy. 2018; 22: 4. Available from: https://www.independent.org/publications/tir/article.asp?id=1285.

34.