Stability and bifurcations in a general Cournot duopoly model with distributed time delays

This paper is devoted to the analysis of a Cournot game, described by a nonlinear mathematical model with four distributed time delays, modelling the behavior of two interacting firms on the market. For each firm, a delay for its own production and one for the production of the competitor are introduced. The analysis of the stability of the four equilibrium points is accomplished. The three equilibria with at least one zero component are shown to be unstable, regardless of the choice of time delays. For the stability and bifurcation analysis of the positive equilibrium, four scenarios are considered to highlight the role played by the time delays: only competitor's delays for both players, equal delays for both players, no delays for one player and only own delays for both players. Numerical simulations are performed to illustrate the theoretical results.