Complex system and influence of delayed decision on the stability of a triopoly price game model

A triopoly price game model has been established based on nonlinear and economics theories in this paper, and all 3 firms of triopoly market are supposed to make a price decision with bounded rationality. By discrete dynamical system theory and jury condition, we obtain the expression of Nash equilibrium point's stable region. Then traditional two-dimensional and creative three-dimensional diagrams of the local stable region are given by numerical simulation, and both 2D and 3D diagrams showed us some law about the Nash equilibrium point's stable region. First, the number of time-delay decision makers has no necessary relationship with system stability; Second, under the same number of time-delay decision makers, the delay parameter has a positive influence of system stability, i.e., the price making relying more on current period profits can lower the system risk of falling into chaos. These results have significant theoretical and practical value to the price making of firms in related markets.