Nonlinear Dynamics in the Cournot Duopoly Model with Uncertain Price

This paper introduces a competition in the Cournot duopoly game where the players adopt uncertain price functions. In contrast with other studies found in the literature, the aim of each player in this game is to maximize its expected profit along with minimizing its variance. The optimization objective functions in this game are linear combinations of the expected profit and its variance for each firm. The firms are assumed to adjust their outputs adaptively based on bounded rationality, leading to a discrete-time nonlinear system. The game’s map’s dynamic characteristics are analyzed in detail, including supporting the obtained results with numerical evidence such as contact bifurcations, basins of attraction and absorbing areas. The obtained results show that increasing the price uncertainty parameter or a firms’ adjustment speed can destabilize the Cournot–Nash equilibrium and drive the system toward cyclical or chaotic fluctuations. These results provide us a more profound understanding of how uncertainty and adaptive behavior work together to produce unexpected changes in prices and production in real markets.