To the analytical investigation of the convergence conditions of the processes of reflexive collective behavior in oligopoly models

A study of the dynamics of the collective behavior of interconnected rational agents under conditions of incomplete information is presented. Statements are proved that permit one to unify the conditions for convergence to equilibrium for two trajectories of the response of agents to the expected actions of the environment: (1) “classic” optimization behavior, in which agents try to choose optimal responses, ignoring possible current “negative states;” (2) behavior that guarantees each agent motion towards the objective and nonnegative current states. The application of the results obtained in the Cournot and Stackelberg oligopoly models with reflexive behavior of agents is shown. Sufficient conditions for the convergence of processes of collective behavior in an oligopoly with an arbitrary number of Stackelberg leaders are obtained.