The Game Study Of Production And Price Competition Based On Quadratic Cost Function

With the development of e-retail and digital technology,the market structure of oligopoly is gradually formed in many industries.In the real market,the cost of enterprises may show the trend of non-linear change,and the simple linear function cannot fully describe the cost structure of enterprises.Quadratic cost structure and primary cost structure have different effects on the stability of the game system,and the change of cost structure will also affect enterprises’ decision of in the market competition.Based on Cournot duopoly game model and Bertrand duopoly game model,this paper introduces nonlinear quadratic cost function,carries out the mathematical derivation and analysis of the model,studies the trend of production and price change in game system,and the influence factors of production and price changes.And makes numerical simulation by MATLAB software to verify the calculation results.Finally,put forward the policy proposal to the oligopoly industry,and take in China’s express delivery industry as an example,to make a realistic analysis of the competition behaviors,and based on the cost structure,put forward corresponding suggestions of reasonable decision-making and orderly competition in the express delivery industry.This paper mainly includes the following aspects.(1)Taking the quadratic cost function into consideration,to construct the Cournot duopoly game model and Bertrand duopoly game model,and explore the dynamic behavior of the game system.Firstly,we carry out the mathematical derivation and calculate the Nash equilibrium point and stability domain of the model.(2)On the basis of the production game model and price game model,a series of complex dynamics analysis was made.Through the numerical simulation of MATLAB,the production bifurcation diagram,price bifurcation diagram,stability domain were obtained.The influence of some parameters in the model,such as production/price adjustment speed and cost change rate on the stability of duopoly game system,was mainly studied.The different influences of the linear cost change rate and quadratic cost change rate were analyzed,and the change of the system under the quadratic cost and the linear cost structure was compared.Therefore,enterprises should make correct analysis and judgment of product cost structure,and maintain stability and orderly development of the market by strengthening control of cost.(3)Based on the results of theoretical research,the policy proposal were put forward to the oligopoly industry,and China’s express delivery industry with typical quadratic cost function was taken as an example,the scale competition and price competition behaviors among express delivery oligarchs were analyzed,and suggestions about rational decision-making and orderly competition were proposed based on cost structure.