JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (11): 63-70.doi: 10.6040/j.issn.1671-9352.0.2019.159

Previous Articles     Next Articles

Dynamic analysis of game model considering advertising spillover effect

LU Zheng-yu, ZHOU Wei*, YU Huan-huan, ZHAO Na   

  1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Published:2019-11-06

PDF (PC)

407

Abstract: Based on the bounded rationality, the dynamic adjustment game model of bounded rationality is established by introducing the parameters of advertising spillover effect, adjustment speed and advertising promotion effect. Firstly, the stability of the system is discussed based on the eigenvalues of Jacobi matrix and Jury criterion. Secondly, the dynamic evolution process of the system under the parameters of advertising spillover effect and adjustment speed is analyzed by the bifurcation diagram of single and double parameters, the maximum Lyapunov index diagram and the attractor basin. The results show that when the adjustment speed of advertising spillover effect is slower, the system will be in a more stable state, and will be in a stable state. In addition, when the adjustment speed increases, the system appears chaos from period and attractor coexistence, which indicates that the market will be chaotic.

Key words: bounded rationality, advertising spillover effect, bifurcation, state of chaos

CLC Number: 

  • O193
[1] 张庶萍.竞争环境下的广告策略研究[D].天津:天津大学,2005. ZHANG Zheping. Research on advertising strategy in competitive environment[D].Tianjin: Tianjin University, 2005.
[2] 张纪康.广告经济学实用教程[M].上海:上海远东出版社,1999:147. ZHANG Jikang. Practical course in advertising economics[M].Shanghai: Shanghai Far East Publishing House, 1999:147.
[3] LITTLE J D C. Aggregate advertising models: the state of the art[J]. Operational Research, 1979, 27(4):629-667.
[4] CELLINI R, LAMBERTINI L. Advertising with spillover effects in a differential oligopoly game with differentiated goods[J].Central European Journal of Operations Research, 2003, 11(4):409-423.
[5] QI Jie, WANG Dingwei, DING Yongsheng, et al. Dynamical analysis of a nonlinear competitive model with generic and brand advertising efforts[J]. Nonlinear Analysis: Real Word Applications, 2007, 8(2):664-679.
[6] BENCHEKROUN H. A unifying differential game of advertising and promotion[J]. International Game Theory Review, 2007, 9(2):183-197.
[7] NORMAN G, PEPALL L,RICHARDS D.Generic product advertising, spillovers, and market concentration[J]. American Journal of Agricultural Economics, 2008, 90(3):719-732.
[8] AHMED E, ELSADANY A A, PUU T. On Bertrand duopoly game with differentiated goods[J]. Applied Mathematics and Computation, 2015, 251:169-179.
[9] AGLIARI A, NAIMZADA A K, PECORA N. Nonlinear dynamics of a Cournot duopoly game with differentiated products[J]. Applied Mathematics and Computation, 2016, 281:1-15.
[10] 于维生,于羽.基于伯川德推测变差的有限理性动态寡头博弈的复杂性[J]. 数量经济技术经济研究,2013,25(2):126-137. YU Weisheng, YU Yu. The complexity of bounded rational dynamic oligarch game based on Bertchuandes prediction of variation[J].Quantitative Economic and Technological Economic Research, 2013, 25(2):126-137.
[11] 田丽娜.考虑溢出效应的互补品企业广告决策研究[D]. 重庆:重庆大学, 2010. TIAN Lina. Research on advertising decisions of complementary products considering spillover effect[D]. Chongqing: Chongqing University, 2010.
[12] COUGHLAN A T. Distribution channel choice in a market with complementary goods[J]. International Journal of Research in Marketing, 1987, 4(2):85-97.
[13] ZHANG H. Vertical information exchange in a supply chain with duoply retailers[J]. Production and Operations Management, 2002, 11(4):531-546.
[14] 马西莫·莫塔.竞争政策:理论与实践[M].上海:上海财经大学出版社,2006:466. MOTA Massimo. Competition policy:theory and practice[M]. Shanghai:Shanghai University of Finance and Economics Press, 2006:466.
[15] BHASKARAN S R, GILBERT S M. Selling and leasing strategies for durable goods with complementary products[J]. Management Science, 2005, 51(8):1278-1290.
[16] CHU W. Demand signaling and screening in channels of distribution[J]. Marketing Science, 1992,11(4):327-347.
[17] XIE J, WEI J C. Coordinating advertising and pricing in a manufacturer-retailer channe[J]. European Journal of Operational Research, 2009, 197(2):785-791.
[18] KADIYALI V. Entry its deterrence and its accommodation: a study of the U.S. photographic film industry[J]. RAND Journal of Economics, 1996, 27(3):452-478.
[19] ZHANG Yahui, ZHOU Wei, CHU Tong, et al. Complex dynamic analysis for two-stage Cournot duopoly game of semi-collusion in production[J]. Nonlinear Dynamics, 2018, 91(2):819-835.
[20] ASKAR S S, ALSHAMRANI A M, ALNOWIBET K. Dynamic Cournot duopoly games with nonlinear demand function[J]. Applied Mathematics and Computation, 2015, 259:427-437.
[1] CHEN Lu, ZHANG Xiao-guang. Research of an epidemic model on adaptive networks [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(9): 76-82.
[2] 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.
[3] LI Le-le, JIA Jian-wen. Hopf bifurcation of a SIRC epidemic model with delay [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(1): 116-126.
[4] LIU Hua, YE Yong, WEI Yu-mei, YANG Peng, MA Ming, YE Jian-hua, MA Ya-lei. Study of dynamic of a discrete host-parasitoid model [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(7): 30-38.
[5] ZHANG Dao-xiang, SUN Guang-xun, MA Yuan, CHEN Jin-qiong, ZHOU Wen. Hopf bifurcation and spatial patterns in a delayed diffusive predator-prey system with Holling-III functional response and linear harvesting effect [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(4): 85-94.
[6] DONG Ya-ying. Global bifurcation structure in a predator-prey model with a spatial degeneracy [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(4): 76-84.
[7] BAI Bao-li, ZHANG Jian-gang, DU Wen-ju, YAN Hong-ming. Dynamic behavior analysis of a stochastic SIR epidemic model [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(4): 72-82.
[8] LI Yue-xia, ZHANG Li-na, ZHANG Xiao-jie. Bifurcation structures for the 2-D Lengyel-Epstein system [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(8): 74-78.
[9] SHI Xue-wei, JIA Jian-wen. Study on an SIR epidemic model with information variable and graded cure rate [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(3): 51-59.
[10] LI Xiao-yan, XU Man. Existence and multiplicity of nontrivial solutions of Dirichlet problems for second-order impulsive differential equation [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(12): 29-35.
[11] LI Hai-xia. Coexistence solutions for a predator-prey model with additive Allee effect and a protection zone [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(09): 88-94.
[12] WU Dai-yong, ZHANG Hai. Stability and bifurcation analysis for a single population discrete model with Allee effect and delay [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(07): 88-94.
[13] ZHANG Lu, MA Ru-yun. Bifurcation structure of asymptotically linear second-order #br# semipositone discrete boundary value problem#br# [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 79-83.
[14] FENG Xiao-zhou1,2, NIE Hua2. Bifurcation solutions and stability of a predator-prey system with predator saturation and competition [J]. J4, 2012, 47(5): 103-107.
[15] CHEN Si-yang, LIU Xiao-na. Stability and bifurcation analysis of the model with interference and piecewise constant variables [J]. J4, 2012, 47(11): 109-118.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] LIU Shuang-gen, LI Dan-dan, LI Xiao. Elliptic curve scalar multiplication algorithm based on bronze ratio addition chain[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(11): 12 -19 .
[2] XIONG Xing-guo, LU Ling-xia. MV-algebra valued metric-based fuzzy rough sets[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(11): 81 -89 .
[3] 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 .
[4] ZHENG Jing-zhu, YANG Hai-ning, SU Ye, QIN Jing. A blindly public verifiable outsourcing scheme for matrix multiplication[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(11): 1 -11 .
[5] WU Zheng-xiang, LI Bao-ku. Equilibrium strategies of dual-channel supply chain considering the retailers social comparison behavior[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(11): 20 -34 .
[6] ZHANG Ke-yong, LI Chun-xia, YAO Jian-ming, LI Jiang-xin. Decision-making and coordination of green supply chain with risk aversion under government subsidies[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(11): 35 -51 .
[7] FENG Dan-dan, WU Hong-bo. Open remote neighborhoods of topological systems and their applications[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(11): 90 -96 .
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd