Dynamics Research On A Class Of Oligopolistic Output Game And Mixed Model

The firms’ competition in oligopolistic market has been one of the hottest fieldsresearched by economists. Applying the bifurcation and chaos theory in nonlinearscience and relevant economics theory, this dissertation conducts a deep and detailedstudy for a class of oligopoly game models. First, the three oligopolists’ discretedynamic system model with different expectations is established. Then by introducingdelay decision, the four oligopolists’ discrete dynamic system model with differentexpectations is built. Both the two models regard output as the decision variable. Inpractice, some firms take the competition strategy of regarding output as the decisionvariable, while some regard price as the decision variable. Furthermore, there aredifferences between oligopolists’ products. So the Cournot-Bertrand mixed model isestablished for this market situation. The complex dynamic behaviors showed by thechange of the parameters in the three different type’s models are analyzed. And someconclusions having theoretical significance and practical value are obtained.Throughout the full dissertation, the contributions are listed as follows:1. In microeconomics, both the total cost function and the demand function arenonlinear. The total cost curve is analogous to the cubic function whose inflectionpoint lies in the first quadrant, i.e., the slope of total cost function is alwaysnon-negative in its definitional domain. Also it decreases to zero on the left side of theinflection point and gradually increases while on the right side of the inflection point.This dissertation introduces the cubic cost curve for the first time. Then, the nonlinearoligopoly game model via combining with the quadratic demand function is set up.2. Since the decision-making types of firms are different, the expectations of thefuture will be also different. The three oligopolists’ output game model and the fouroligopolists’ output game model are set up under the assumption that firms have staticexpectation, adaptive expectation, boundedly rational expectation, and delayedbounded rationality expectation, respectively. The influence that the parameters’changes of firms having different expectations exert to the stability of the market isdiscussed, and the effect of the delay decision on the system is also analyzed. 3. Based on the Cournot model and the Bertrand model, this dissertation studies amore generic oligopoly game model, i.e., the Cournot-Bertrand mixed model. In thismodel, the first firm belongs to the Cournot-type and regards output as the decisionvariable; while the second firm belongs to the Bertrand-type and regards price as thedecision variable. The influence that the changes of the output adjustment speed andthe price adjustment speed exert on the market stability is analyzed.4. This dissertation studies the influence that the differences of products exert onmarket competition in Cournot-Bertrand mixed model. The results show that,different degree of oligopolists’ product differences can make the market evolve todifferent states. The firms purposely seeking large differences will lead the market toinstability, even getting into the chaotic state which is adverse to all firms.5. By controlling the chaos phenomenon appeared on the market, the bifurcationand chaos phenomena are delayed or eliminated; and the system is stabilized to theNash equilibrium, i.e., the market goes back to orderly competition. Finally, theeconomic explanation of the chaos control is offered, and the theoretical referencesfor real economic management problems are also provided.