
L.V. Zhukovskaya Gametheoretic approach to modeling of family relations in conditions of transformation of social and economic system 

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 sociodemographic 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 socioeconomic 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 gametheoretic 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. 1226. 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: EconInform. 318 p. 2. 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