articles

The article examines a game-theoretic model describing the interaction between two firms selling identical products, a classic duopoly model. The model expresses competition between the firms, as the players’ objective functions express their utility (profit) and are mutually inconsistent, i. e., a noncooperative, zero-sum game is considered. The players’ objective functions are formed based on the linear inverse demand function for the product and the linear cost functions of the participating firms. The solution to the game is a Nash equilibrium, determined using a system of first-order necessary optimality conditions. Unlike the classical approach, the model incorporates two new aspects. First, players are considered reflexive, meaning each player hypothesizes the counterparty’s likely response, which is formally expressed as a conjectural variation – the expected change in one player’s output in response to a single increase in the output of the other. Second, an aggregative game in a duopoly model, in which the players’ objective functions are interdependent, is analyzed from the perspective of controlling the behavior of one player by manipulating their mental representations of the other player’s intentions. The analysis of the game is based on a reflexive model of player behavior, in which players sequentially predict each other’s representations, resulting in the identification of a mental model of one player that is optimal from the perspective of the other player. An iterative procedure is proposed for inducing this mental model in the controlled player by creating phantom instances of the controlling player. Numerical experiments illustrate various aspects of the mental control process, whereby the technical characteristics of the player firms, such as their production volumes, interact with the mental behavioral parameters of decision makers, forming a cyber-physical system.