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.

本文致力于分析古诺博弈，该博弈由具有四个分布式时间延迟的非线性数学模型描述，对市场上两家互动公司的行为进行建模。对于每家公司，引入了其自身生产的延迟和竞争对手的生产延迟。完成了四个平衡点的稳定性分析。具有至少一个零分量的三个平衡被证明是不稳定的，无论时间延迟的选择如何。对于正均衡的稳定性和分岔分析，考虑了四种情况来突出时间延迟所起的作用：两个玩家只有竞争对手的延迟，两个玩家的延迟相等，一个玩家没有延迟，两个玩家只有自己的延迟.