The application and complexity analysis about a high-dimension discrete dynamical system based on heterogeneous triopoly game with multi-product

In production practice, firms usually produce multi-products rather than single products to obtain cost-saving advantages, cater for the diversity of consumer tastes and provide a barrier to entry. Based on nonlinear and economics theories, this paper establishes a discrete triopoly dynamical model which considers multi-product firms with heterogeneous expectations: naïve, adaptive and bounded rationality expectations. The discrete model is described by a 6-dimensional dynamical system. Thesis explores the path of the complexity of evolution and its intrinsic regularity, studies the influence of parameter change on the sensitivity level. The stable conditions of Cournot Nash equilibrium point are analyzed. The route to complex dynamics is investigated using 2-D and creative 3-D bifurcation diagrams by numerical experiment. The results show: the adaptive parameters can modify the stability of the market, but cannot lead to chaos independently; the bounded rationality parameters can arouse chaos for the whole market; larger differentiated degree of multi-product can suppress instability which is caused by adaptive and bounded rationality adjustment parameters. These results have significant theoretical and practical value to multi-product triopoly game with heterogeneous expectations in related markets.