基于创新驱动的天然气三寡头垄断市场动态微分博弈定价模型  

A Dynamic Differential Game Pricing Model for the Natural Gas Triopoly Market Based on Innovation Drive

作　　者：李升泉 龙登高 张荣[1] LI Shengquan;LONG Denggao;ZHANG Rong(Economics and Business Administration,Chongqing University, Chongqing 400030,P.R.China;School of Social Sciences,Tsinghua University, Beijing 100083,P.R.China)

机构地区：[1]重庆大学经济与工商管理学院,重庆400030 [2]清华大学社会科学学院,北京100083

出　　处：《应用数学和力学》2018年第12期1426-1442,共17页Applied Mathematics and Mechanics

基　　金：国家社会科学基金(16BGL136);国家自然科学基金(71772019);中央高校基本科研业务费(CQDXWL-2013-088; 106112017CDJXY020002)~~

摘　　要：针对天然气生产商三寡头垄断市场,基于知识创新所产生的成本降低和降价决策反应时滞,建立了定价决策动态微分博弈模型.模型分析发现:知识创新周期不变时,企业可通过调整知识创新投入产出强度来降低成本,并据此实施降价策略,随着创新投入产出强度的改变,系统会出现Hopf分岔,且有唯一的Nash平衡点;当创新投入产出强度不断增加时,系统会达到并保持平衡状态;而创新投入产出强度不断降低时,系统会出现周期解,进而增大周期运动幅度,市场出现无序竞争状态.数值模拟印证了理论推导结果.该研究对于三寡头垄断市场中,各天然气生产商有效实施创新驱动战略具有积极的参考价值.The triopoly market of natural gas manufacturers was studied,and a dynamic differential game pricing model was established based on the cost reduction resulting from knowledge innovation and the response lag in the price reduction decision. Model analyses indicate that,when the period of knowledge innovation remains constant,enterprises can reduce costs by adjusting the input and output intensities of knowledge innovation and implement price strategies accordingly. With the variation of the input and output intensities of knowledge innovation,the Hopf bifurcation and a single Nash equilibrium point will emerge in the system. With continuous increases of the input and output intensities,the system will reach and maintain an equilibrium; with continuous decreases of the input and output intensities,the system will yield a periodic solution,the range of the periodic motion will expand,and the market will fall into a chaotic competitive state. Numerical simulations confirm the theoretically derived results. This study provides a reference for the natural gas manufacturers within the triopoly market to effectively implement innovation-driven strategies.

关 键 词：天然气 寡头垄断 知识创新 定价 动态博弈 

分 类 号：O225[理学—运筹学与控制论]