Analysis of conjectural variations in cyber-physical oligopoly game system under different models of consumer demand and firm’s costs

The game-theoretic problem of analyzing volumetric competition in an oligopoly is considered for the case of demand and cost functions of a general type. The cyberphysical system is investigated on the basis of presumptive variations, i.e. the assumptions of the players about the impact of their actions on the actions of the counterparty. The hierarchy of players' assumptions determines their stratification by leadership levels into zero-level leaders (considered as followers) who do not take into account the actions of the environment and are players with zero conjectural variation; leaders of the first level, who believe that the environment includes leaders of the zero level; leaders of an arbitrary level, who consider other players to be leaders of the previous level. The conjectural variation determines the player's level of leadership in the game and characterizes the player's optimal response to the counterparty's strategy. A comparative analysis of the players' assumptions is carried out in cases of linear and power-law functions of customer demand, as well as for various types of cost functions (linear, power-law, quadratic). The main research question is to model a cyber-physical system in the context of the influence of the types of consumer demand functions and player costs on the value of the total conjectural variation in the oligopoly game model. It is established that in the linear-quadratic model, the effect of an increase in player sales on a decrease in the sales volume of the environment is less radical than in the linear model. In the power-law model, there is a greater importance of the modulus of decrease in the sales volume of the environment relative to the linear model. The quadratic-power model is similar in characteristics to the negative-scale power model.