Abstract. 

The article presents a methodology for modeling decision-making processes in complex controlled dynamic systems: the implementation of the idea of balanced (equilibrium) systems and the formation of a new mechanism that contributes to solving the problems of equilibrium stability. These developments are based on economic and mathematical modeling using a synthesis of scientific approaches to system analysis, economics, law, game theories, operations research and decision making. The linear-quadratic positional differential game of many people is considered. Coefficient criteria have been established at the fulfillment of which in the game there is a balance of sanctions and counter-sanctions and at the same time there is no generally accepted Nash equilibrium. The economic-legal model of active equilibrium through the legal concept of sanctions is considered, which expands the field of practical application of this class of tasks.

Keywords: 

managed complex system, sanctions, counter-sanctions, balance of sanctions of counter-sanctions, active equilibriums, stability, efficiency, Pareto maximum.

PP. 39-52.

DOI: 10.14357/20790279200205

 

References

1. Waisbord E.M. 1974. O koalitsionnykh differentsial’nykh igrakh, Differentsial’nyye uravneniya [On coalition differential games”, Differential equations] 10:4. 613–623.

2. Waisbord E.M., Zhukovsky V.I. 1980. Vvedeniye v differentsial’nyye igry neskol’kikh lits i ikh prilozheniya [Introduction to the differential games of several people and their applications] Soviet Radio. M.

3. Voevodin V.V., Kuznetsov Yu.A. 1984. Matritsy i vychisleniya [Matrices and calculations] Nauka. M.

4. Zhukovsky V.I., Chikriy A.A. 2017. Differentsial’nyye uravneniya. Lineynokvadratichnyye differentsial’nyye igry, Uchebnoye posobiye dlya VUZov [Differential equations. Linear-square differential games, Textbook for High Schools] Yurayt. M.

5. Zhukovskaya L.V. (Biryukova L.V.) 1996 Ravnovesiye ugroz i kontrugroz pri neopredelennosti [Balance of threats and counter-threats under uncertainty] / Abstract. diss .... Candidate of physico-mathematical sciences. SPb.15 p.

6. Kleiner G.B., Rybachuk M.A. 2017. Sistemnaya sbalansirovannost’ ekonomiki: monografiya [Systemic balance of the economy: monograph] Central Economics and Mathematics Institute of the Russian Academy of Sciences. M. Scientific Library.

7. Leist O.E. 1962. Sanktsii v Sovetskom prave [Sanctions in Soviet law. State publishing house of legal literature] M.

8. Mamedov M.B. 1983. O ravnovesii po Neshu situatsii, optimal’noy po Pareto [On the Nash equilibrium of a Pareto optimal situation] Izv. Academy of Sciences of Azerbaijan. Series of physical and technical. Sciences 4: 2. 11–17.

9. Podinovsky V.V., Nogin V.D. 2007. Paretooptimal’nyye resheniya mnogokriterial’nykh zadach [Pareto-optimal solutions of multicriteria problems] Fizmatlit. M.

10. Case J.H. 1974. A class of games having Pareto optimal Nash equilibrium J. Optimiz. Theory Appl. 13:3. 378–385.

11. Nash J. 1951. Non-cooperative games. Annales of Mathematics. 54. 286–295.

12. Zhukovskii V.I. 1985. Some Problems of Non- Antagonistic Differential Games. Mathematical Method in Operation Research. Academy of Sciences. Bulgaria. Sofia. 103–195.