The Study And Application Of Cournot-Bertrand Mixed Model Based On Nonlinear Theory

Oligopoly game model, with its complexity and diversity, attracts mathematicians,economists and management scientists’ research attention. In real economic activity, be-sides the Cournot model, in which firms choose the output as the decision variable, andthe Bertrand model, in which firms choose the price as the tool of competition, there arealso the situations, in which there coexist two groups of firms, the first of which optimallyadjust output and the other one optimally adjust their prices to ensure maximum profit,which is known as the Cournot-Bertrand mixed model. In this paper, based on the researchat home and abroad, the Cournot-Bertrand mixed models are analyzed by comparing withCournot and Bertrand models, using the game theory, dynamic economics and nonlineardynamics methods. This research can help us to better understand the competition andevolutionary mechanism of the oligopoly market. The main content of this dissertation isas follows:1. With the assumption that there is a certain degree of diferentiation betweenthe products ofered by firms, whose decision-making principles are bounded rational,duopoly Cournot, Bertrand and Cournot-Bertrand mixed models are built. The existenceand local stability of Nash equilibrium point are investigated and the stability regionis plotted. The complex dynamical behaviors of the Cournot, Bertrand and Cournot-Bertrand mixed models are further studied, including bifurcation scenarios, the largestLyapunov exponent, strange attractor, butterfly efect, etc. The influences of the parame-ters on the systems’ performance are discussed from the perspective of economics.2. The profit, price, output, consumer surplus and social welfare of the Cournot,Bertrand and Cournot-Bertrand mixed models in the Nash equilibrium point are com-pared investigated. The average output, average price and average profits in the periodicsolution and chaos are also studied. The diferent characters of the three kind of modelsare summarized. The efects of the product diferentiation on systems’ stability are alsoanalyzed.3. A Cournot-Bertrand mixed model with delayed bounded rationality expectationis established. The influences of the weight of delay on the stability of Nash equilibriumpoint are studied. Through comparing with the system which does not contain the delay, the results show that the system with delay can be controlled from chaos to stability orperiod states by reasonably choosing the weight of delay.4. A triopoly Cournot-Bertrand mixed model which is composed of one state-ownedenterprise and two private enterprises is constructed. The existence and local stability ofNash equilibrium point and the bifurcations of the system with variety of the decisionparameters are investigated. The influences of initial values on the system are also con-sidered and the basins of attraction are given. The influences of the parameters and ini-tial values on the system dynamics evolution are analyzed, and these results can providedecision-making reference for the enterprises’ managers and decision makers.