On the Concept of Equilibrium in Sanctions and Countersanctions in a Differential Game

This paper develops the methodology for modeling decision processes in complex controlled dynamic systems. The idea of balancing such systems (driving them to equilibrium) is implemented, and a new mechanism for the equilibria’s stability is proposed. Such an approach involves economic–mathematical modeling jointly with systems analysis methods, economics, law, sociology, game theory, management, and performance measurement. A linear-quadratic positional differential game of several players is considered. Coefficient criteria under which the game has an equilibrium in sanctions and countersanctions and, simultaneously, no Nash equilibrium are derived. The economic and legal model of active equilibrium is studied through the legal concept of sanctions, which enlarges the practical application of this class of problems.