政府征税与补贴Bertrand博弈模型的动力学分析

doi:10.6040/j.issn.1671-9352.0.2018.530

《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (11): 52-62.doi: 10.6040/j.issn.1671-9352.0.2018.530

政府征税与补贴Bertrand博弈模型的动力学分析

曹慧荣¹,周伟^1*,褚童²,周洁¹

1. 兰州交通大学数理学院, 甘肃兰州 730070;2. 浙江财经大学法学院, 杭州浙江 310018

发布日期:2019-11-06
作者简介:曹慧荣(1991— ),女,硕士研究生,研究方向为非线性动力学与博弈论. E-mail:1466322946@qq.com*通信作者简介:周伟(1981— ),男,博士,副教授,研究方向为非线性动力学与博弈论. E-mail:1838929181@qq.com
基金资助:
国家自然科学基金资助项目(61364001);兰州交通大学青年科学研究基金项目(2015029);甘肃省高等学校科研项目(2015B-047)

Dynamic analysis of Bertrand game model about taxation of government and subsidy

CAO Hui-rong ¹, ZHOU Wei^1*, CHU Tong², ZHOU Jie¹

1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China;
2. School of Law, Zhejiang University of Finance and Economics, Hangzhou 310018, Zhejiang, China

Published:2019-11-06

摘要/Abstract

摘要： 在政府同时实施征税与补贴政策的背景下,基于有限理性建立了动态Bertrand博弈模型。利用Jury条件分析了系统平衡点的局部渐近稳定性,均衡点失稳后系统的演化过程采用数值模拟的方法进行讨论。讨论发现,企业利润在Nash均衡态最优,价格调整速度过高或政府给予的补贴份额过低均使系统进入混沌,企业利润将出现负增长。为了保证企业处于盈利模式,采用状态反馈和参数调节控制策略使系统长期处于Nash均衡。此外,分析吸引盆内部结构发现,过高的调整速度使系统发生全局分岔,初始决策的选择出现不可预测性。

关键词: Bertrand博弈模型, 征税与补贴, 分岔, 混沌控制

Abstract: In the context of government implements both subsidy and taxation policies, a dynamics Bertrand game model is established based on bounded rationality. The local asymptotic stability of equilibrium points of the system is analyzed using Jury conditions, the evolution process of the system after equilibrium point instability is discussed by numerical simulation method. It is found that enterprise profit is optimal in Nash equilibrium. The high speed of price adjustment or the low share of government subsidies make the system chaotic, and the profits of enterprises will increase negatively. In order to ensure that enterprises are in the profit mode, the state feedback and parameter adjustment control strategy are adopted to keep the system in Nash equilibrium for a long time. In addition, by analyzing the internal structure of the attraction basin, it is found that the high adjustment speed makes the system bifurcate globally, and the choice of initial decision-making appears unpredictable.

Key words: Bertrand game model, taxation and subsidy, bifurcation, chaos control

中图分类号:

O193

曹慧荣,周伟,褚童,周洁. 政府征税与补贴Bertrand博弈模型的动力学分析[J]. 《山东大学学报(理学版)》, 2019, 54(11): 52-62.

CAO Hui-rong , ZHOU Wei, CHU Tong, ZHOU Jie. Dynamic analysis of Bertrand game model about taxation of government and subsidy[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(11): 52-62.

参考文献

[1] KOO W W, UHM I H. Effects of dumping vs anti-dumping measures the US trade remedy laws applied to wheat imports from Canada[J]. Journal of World Trade, 2007, 41(6): 1163-1184.
[2] 严俊樑, 钟根元. 完全信息下实行反倾销措施与补贴措施的静态博弈分析比较[J]. 陕西科技大学学报(自然科学版), 2008, 26(6): 167-171. YAN Junliang, ZHONG Genyuan. Difference research between AD rates and subsidy of static game under complete information[J]. Journal of Shaanxi University of Science & Technology, 2008, 26(6): 167-171.
[3] 翁世洲, 朱俊. 政府反倾销与补贴战略实施博弈分析[J]. 现代商贸工业, 2017(8): 43-44. WENG Shizhou, ZHU Jun. Game analysis on the implementation of governments anti-dumping and subsidy strategy[J]. Modern Business Trade Industry, 2017(8): 43-44.
[4] 江东坡, 朱满德. 双寡头竞争下的反倾销与补贴政策比较[J]. 华东经济管理, 2015, 29(5): 97-102. JIANG Dongpo, ZHU Mande. Comparison of antidumping tariff and production subsidy under oligopoly[J]. East China Economic Management, 2015, 29(5): 97-102.
[5] COURNOT A A. Recherches sur les principes mathematiques de la theorie des richesses[M]. Paris: Hachette Livre-Bnf, 1838.
[6] RAND D. Exotic phenomena in games and duopoly models[J]. Journal of Mathematical Economics, 1978, 5(2): 173-184.
[7] DAY D, CHEN P. Nonlinear dynamics and evolutionary economics[C] //The Robustness of Bubbles and Crashes in Experimental Stock Markets, [S.l.] :[s.n.] , 1993.
[8] ELSADANY A A. Dynamics of a Cournot duopoly game with bounded rationality based on relative profit maximization[J]. Applied Mathematics and Computation, 2017, 294: 253-263.
[9] TRAMONTANA F, ELSADANY A A, XIN B G, et al. Local stability of the Cournot solution with increasing heterogeneous competitors[J]. Nonlinear Analysis: Real World Applications, 2015, 26: 150-160.
[10] PENG Y, LU Q, XIAO Y. A dynamic Stackelberg duopoly model with different strategies[J]. Chaos, Solitons & Fractals, 2016, 85: 128-134.
[11] AHMED E, ELSADANY A A, PUU T. On Bertrand duopoly game with differentiated goods[J]. Applied Mathematics and Computation, 2015, 251: 169-179.
[12] BRIANZONI S, GORI L, MICHETTI E. Dynamics of a Bertrand duopoly with differentiated products and nonlinear costs: analysis, comparisons and new evidences[J]. Chaos, Solitons & Fractals, 2015, 79: 191-203.
[13] FANTI L, GORI L, MAMMANA C, et al. The dynamics of a Bertrand duopoly with differentiated products: synchronization, intermittency and global dynamics[J]. Chaos, Solitons & Fractals, 2013, 52: 73-86.
[14] CAVALLI F, NAIMZADA A. A Cournot duopoly game with heterogeneous players: nonlinear dynamics of the gradient rule versus local monopolistic approach[J]. Applied Mathematics and Computation, 2014, 249: 382-388.
[15] MA J H, GUO Z B. The influence of information on the stability of a dynamic Bertrand game[J]. Communications in Nonlinear Science and Numerical Simulation, 2016, 30(1/2/3): 32-44.
[16] ZHOU J, ZHOU W, CHU T, et al. Bifurcation, intermittent chaos and multi-stability in a two-stage Cournot game with R& D spillover and product differentiation[J]. Applied Mathematics and Computation, 2019, 341: 358-378.
[17] 姚洪兴, 王梅. 动态Bertrand模型的复杂现象与混沌控制[J]. 陕西师范大学学报(自然科学版), 2015, 43(2): 24-27. YAO Hongxing, WANG Mei. The complex phenomena and the chaos control of Bertrand model[J]. Journal of Shaanxi Normal University(Natural Science Edition), 2015, 43(2): 24-27.
[18] BISCHI G I, NAIMZADA A. Global analysis of a dynamic duopoly game with bounded rationality[J]. Advances in Dynamic Games and Applications, 2000, 5: 361-385.

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed

政府征税与补贴Bertrand博弈模型的动力学分析

Dynamic analysis of Bertrand game model about taxation of government and subsidy

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 7

多维度评价

本文评价

推荐阅读 6

[1]	路正玉,周伟,于欢欢,赵娜. 考虑广告溢出效应的博弈模型的动力学分析[J]. 《山东大学学报(理学版)》, 2019, 54(11): 63-70.
[2]	刘华,叶勇,魏玉梅,杨鹏,马明,冶建华,马娅磊. 一类离散宿主-寄生物模型动态研究[J]. 山东大学学报（理学版）, 2018, 53(7): 30-38.
[3]	白宝丽,张建刚,杜文举,闫宏明. 一类随机的SIR流行病模型的动力学行为分析[J]. 山东大学学报（理学版）, 2017, 52(4): 72-82.
[4]	鞠培军. 广义Lorenz系统全局稳定的充要条件及其在混沌控制中的应用[J]. J4, 2012, 47(10): 97-101.
[5]	张伟强,刘扬正*. 统一超混沌系统的构建与电路实现[J]. J4, 2011, 46(7): 30-34.
[6]	侯强，靳祯. 基于比率且包含食饵避难的HollingTanner模型分析[J]. J4, 2009, 44(3): 56-60 .
[7]	刘华,刘志广,苏敏,李自珍, . 聚集效应对宿主—寄生物种群模型动态行为的影响[J]. J4, 2008, 43(8): 31-34 .