Abstract.

In the article presents the results of research on the dynamics of family structures and relationships that affect the system of vital activity of the population; state, prospects and possibilities of state regulation of socio-demographic processes in Russia. Formal mathematical models of family relations based on the concepts of the Berge equilibrium that reveals the meaning of the Golden Rule of Morals are constructed: “How do you want people to act with you, do you also with them” and Nash equilibrium – selfish relationships in the family structure of three persons. A new method for formalizing guaranteed solutions in multicriteria control problems for complex socio-economic systems under uncertainty conditions is proposed, based on modifying the principle of the minimax “regret” of Savage. The results of this research allow us to form a new approach to the development of state social programs in the sphere of family relations in particular and in the social sphere in general. The theoretical and practical significance of the results lies in the study of sociodemographic processes using the game-theoretic tools for studying the features of the current dynamics of family relations with a view to determining the possibilities for their state regulation.

Keywords:

social and economic systems, social sphere, sociodemographic processes, family, family structures, multicriteria tasks, Nash equilibrium, Berge equilibrium, the principle of minimizing “regret” Savage, guaranteed solution, vector risk.

PP. 12-26.

DOI: 10.14357/20790279180302

References

1. Rimashevskaya N.M. eds. 2015. Nastoyashee i budushee semyi v menyaushimsya mire [The present and the future of the family in a changing world]. Collective monograph eds. N.M. Rimashevskaya, Moscow: Econ-Inform. 318 p.
2. Engels F. 1884. The origin of the family, private property and the state. Publication of the works of K. Marx and F. Engels. Moscow: 1977, ed. 2, v. 21, pp. 28-178. / Transl. from germ. (Der Ursprung der Familie, des Privateigenthums und des Staats. 150 s.).
3. Engels F. 1877. AntiDuhring Division III. Ch. V “The state, family, education.” Moscow 1977. p. 324-331. / Transl. from germ. (Anti-Dühring. Abteilung III. Ch. V Der Staat, Familie, Bildung. 7 s.).
4. Seung-Yun Oh, Cody T. Ross, Monique Borgerho Mulder, Samuel Bowles «The Decline of Polygyny: An Interpretation» SANTA FE INSTITUTE, 2017- 12-037, 33 р.
5. Nash J.F. 1950. Equilibrium points in N-person game. Proc. Nat. Academ. Sci. USA. V.36.p. 48-49.
6. Hegel G. Only the family as a whole is an individual // Family: A book for reading. Book. 2. Moscow: 1991. p. 143.
7. Guseinov A.A. eds. 1988. Zolotoe pravilo nravstvennosti [The Golden Rule of Morality] Moscow: Young Guard. 1988. 271 p.
8. Guseinov A.A., Zhukovsky V.I., Kudryavtsev K.N. 2016. Matematicheskie osnovi zolotogo pravila nravstvennosti; Teoriya novogo altruisticheskogo uravnoveshivaniya konfliktov v protivopoloznost «egoistichnomy» ravnovesiu po Neshu. [Mathematical foundations of the Golden Rule of Morals:
The theory of a new altruistic balancing of conflicts as opposed to the” selfish “Nash equilibrium]. Moscow: LENAND, 2016, 280 p.
9. Berge K. 1961. The general theory of games of several persons. Moscow: Fizmatgiz,. 126 p. / Transl. from fr. (Théorie générale des jeux de plusieurs personnes. Paris: Gauthier Villars, 1957).
10. Andreeva Т.V. 2004. Semeynaya psihologiya: uchebnoe posobie [Family psychology: Textbook. Allowance]. SPb: Speech. 244 p.
11. Caldwell J.C. 1976. Toward a restatement of demographic transition theory//Population and Development Review. 2(3/4):321-366.
12. Elizarov V.V. 2011. Stimulirovanie rogdaemosti i poddergka semey s detmi v sovremnnoy Rossii Stimulation of fertility and support of families with children in modern Russia. In the collection: Fertility and family planning in Russia: History and prospects. Collection of articles. eds. Troitskaya I.A., Avdeev A.A., Мoscow: Demographic studies, vol. 18, 2011, p. 123-152.
13. Suslov Z.M., Pokrovskaya A.P., Fokin I.A. Rossiya mnogodetnaja: semiya kak odna iz osnov rossiyskoy gosudarstvennosti. Zakonodatelnoe obespechenie sovremennoy demograficheskoy politiki gosudarstva. Materiali k Vserossiyskomu Forumu. Kommitet po voprosam semyi, genshin i detey Gosudarstvennoy Dumi Rossiyskoy Federasii.
[Russia has many children: the family as one of the foundations of Russian statehood. Legislative support of modern demographic policy of the state. Materials for the All-Russian Forum. Committee for Family, Women and Children of the State Duma of the Russian Federation]. / eds. Misulina E.B. Moscow, May 16, 2013. 176 p.
14. Doklad O gosudarstvennoy politike v sfere sem’i, materinstva i detstva. Gossovet O gosudarstvennoy politike v sfere sem’i, materinstva i detstva, [Report On State Policy in the Sphere of Family, Motherhood and Childhood. State Council “On State Policy in the Sphere of Family, Motherhood and Childhood] 17.02.2014, 17 p.
15. Savage L.J. 1951. The Theory of Statistical Decisions) Journal of the American Statistical Association. 46: 55-67.
16. Zhukovskaya L.V. 2001. Matematicheskiye osnovy riska v mnogokriterialnykh zadachakh. Uchebnoye posobiye. [Mathematical foundations of risk in multicriteria problems. Tutorial]. Moscow: Ros ZITLP, 102 p.
17. Zhukovskiy V.I., Zhukovskaya L.V. 2017. Risk v mnogokriterialnih I konflictnih sistemah pri neopredelennosti [Risk in multi-criteria and conflict systems under uncertainty], 3rd ed. Мoscow: URSS: LKI. pp. 78-84. p. 165-168.
18. Podinovskiy V.V., Nogin V.D. 1992. Pareto-optimal’nyye resheniya mnogokriterial’nykh zadach. [Pareto-optimal solutions of multicriteria problems]. Мoscow: Science. p. 29-38, p. 97-117.
19. Vilenskiy P.L., Livshits V.N., Smolyak S.A. 2015. Otsenka effektivnosti investitsionnykh proyektov: Teoriya i praktika: Uchebnoye posobiye. [Evaluation of the effectiveness of investment projects: Theory and practice: Textbook]. Moscow: Poly Print Service, 5th ed. p.704-706.
20. Sorokin P.A. 1956. The American sex revolution. Boston MA: Sargent. 186 p.