The Chaotic Characteristic Analysis Of Multi-product Oligopoly Game Under Different Market Environments

Complex characteristic of oligopoly game has been a hot topic which isresearched by economists and managerialists. However, almost all the complexityresearches of oligopoly models are limited in the case of single-product firm. Inproduction practice, firms usually produce multi-products rather than single productsto obtain cost-saving advantages, cater for the diversity of consumer tastes,risk-aversion and provide a barrier to entry. The traditional large-scale productionmodel based on prediction cannot meet requirements of new situation. The complexdynamics of multi-product oligopoly game becomes a subject to be urgentlyresearched. In this research, the framework of multi-product is introduced todynamical oligopoly game model. The complex characteristics of oligopoly gameunder different economic conditions are studied by economic theory, game theory andnonlinear dynamics theory. This research constructs four dynamical models:Cournot-Bertrand duopoly game model with multi-product, heterogeneous triopolygame model with multi-product, multi-product mixed duopoly game model withpartial privatization and cross-ownership and multi-product Cournot duopoly gamemodel with managerial delegation. The main contents and innovation of the thesis areas follows:1. In this research, Cournot-Bertrand duopoly game model with two-product ispresented. In this model, statuses of two products are unequal. The simulation resultsshow that the economic model is a novel four-dimensional hyperchaotic system. Themarket is more complex and unpredictable than ordinary chaotic system. It is moredifficult for firms to adapt to changes in the drastic market.2. This study establishes a discrete triopoly dynamical model which considersmulti-product firms with heterogeneous expectations. The stable conditions ofCournot Nash equilibrium point are analyzed. The route to complex dynamics isinvestigated using2-D and creative3-D bifurcation diagrams by numericalexperiment. Thesis explores the influence of adaptive parameters, bounded rationalityparameters and differentiated degree of multi-product on the sensitivity level of themodel. 3. This dissertation proposes a multi-product mixed duopoly game with partialprivatization and cross-ownership in which a state owned firm and a private firmcoexist. The existence of Nash equilibrium is examined in this kind of model and itslocal stability is investigated. The complex dynamics of the mixed duopoly model isfurther investigated by3-D bifurcation diagram that is a powerful instrument forstudying multi-dimension dynamical system. The influences of main economicparameters on the sensitivity of the model are investigated.4. This dissertation develops a dynamic multi-product Cournot duopoly model indiscrete time, where each firm has an owner who delegates the output decision to themanager. Each firm has a nonlinear total cost function due to multi-product. TheCournot Nash equilibrium and its local stability are investigated. The tangentialbifurcation and intermittent chaos are reported by numerical simulations. Theintermittent route to chaos of Flip bifurcation and the intermittent route of Flipbifurcation which contains Hopf bifurcation can exist in the system. That meansoligopoly market has been repeatedly disturbed by a series of severe outputfluctuations which results tremendous economic losses of firms and the whole market.Above contents analyze the chaotic characteristics of multi-product oligopolymodel under different market environments, and they are innovative. The referenceand guidance are provided for healthy development and benign competition ofmulti-product market.