2025 01 v.40 72-80
混合双寡头Bertrand博弈模型的复杂动态性研究
基金项目(Foundation):
辽宁省教育厅基本科研项目（JYTMS20231043）
邮箱(Email):
zhhbao@126.com;
DOI:
中文作者单位:
营口理工学院基础教研部;辽宁师范大学数学学院;
摘要(Abstract):
考虑国有企业和私营企业混合竞争的价格博弈模型，他们共同生产某种差异化商品，并且采用有限理性预期原则确定商品的未来价格.建立二维离散动力系统，求解动力系统的边界均衡点和纳什均衡点，并研究它们的稳定性.在数值分析中，通过分岔图、最大Lyapunov指数、奇异吸引子和对初始条件的敏感依赖展示系统的动态性质.最后，利用反馈控制策略对系统进行混沌控制，使系统最终趋于稳定.
关键词(KeyWords):
混合竞争;Bertrand博弈;纳什均衡点;稳定性;混沌控制
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参考文献
[1] 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.
[2] 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.
[3] SARAFOPOULOS G,PAPADOPOULOS K. Complexity in a bertrand duopoly game with heterogeneous players and differentiated goods[C]//Economic and Financial Challenges for Eastern Europe:Proceedings of the 9th International Conference on the Economies of the Balkan and Eastern European Countries in the Changing World(EBEEC)in Athens,Greece,2017. Springer International Publishing,2019:15-26.
[4] ASKAR S S,AL-KHEDHAIRI A. Dynamic investigations in a duopoly game with price competition based on relative prfoit and prfoit maximization[J]. Journal of Computational and Applied Mathematics,2020,367:112464.
[5] XIAO Y, PENG Y, LU Q, et al. Chaotic dynamics in nonlinear duopoly Stackelberg game with heterogeneous players[J]. Physica A:Statistical Mechanics and Its Applications,2018,492:1980-1987.
[6] MA J,SUN L,HOU S,et al. Complexity study on the Cournot-Bertrand mixed duopoly game model with market share preference[J]. Chaos:An Interdisciplinary Journal of Nonlinear Science,2018,28(2):023101.
[7] ASKAR S S. On complex dynamics of Cournot-Bertrand game with asymmetric market information[J].Applied Mathematics and Computation,2021,393:125823.
[8] MATSUMURA T,OGAWA A. Price versus quantity in a mixed duopoly[J]. Economics Letters,2012,116(2):174-177.
[9] NAKAMURA Y. Price versus quantity in a mixed duopoly:The case of relative profit maximization[J].Economic Modelling,2015,44:37-43.
[10] ASKAR S S. Nonlinear dynamic investigations and global analysis of a Cournot duopoly game with two different objectives[J]. Chaos,Solitons and Fractals,2022,155:111711.
[11] NAIMZADA A K,TRAMONTANA F. Dynamic properties of a Cournot-Bertrand duopoly game with differentiated products[J]. Economic Modelling,2012,29(4):1436-1439.
[12] AGIZA H N,ELSADANY A A. Chaotic dynamics in nonlinear duopo ly game with heterogeneous players[J]. Applied Mathematics and Computation,2004,149(3):843-860.
[13] AHMED E,AGIZA H N,HASSAN S Z. On modifications of Puu’s dynamical duopoly[J]. Chaos,Solitons&Fractals,2000,11(7):1025-1028.
[14] PENG Y,XIAO Y,LU Q,et al. Chaotic dynamics in Cournot duopoly model with bounded rationality based on relative profit delegation maximization[J]. Physica A:Statistical Mechanics and its Applications,2020,560:125174.
[2] 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.
[3] SARAFOPOULOS G,PAPADOPOULOS K. Complexity in a bertrand duopoly game with heterogeneous players and differentiated goods[C]//Economic and Financial Challenges for Eastern Europe:Proceedings of the 9th International Conference on the Economies of the Balkan and Eastern European Countries in the Changing World(EBEEC)in Athens,Greece,2017. Springer International Publishing,2019:15-26.
[4] ASKAR S S,AL-KHEDHAIRI A. Dynamic investigations in a duopoly game with price competition based on relative prfoit and prfoit maximization[J]. Journal of Computational and Applied Mathematics,2020,367:112464.
[5] XIAO Y, PENG Y, LU Q, et al. Chaotic dynamics in nonlinear duopoly Stackelberg game with heterogeneous players[J]. Physica A:Statistical Mechanics and Its Applications,2018,492:1980-1987.
[6] MA J,SUN L,HOU S,et al. Complexity study on the Cournot-Bertrand mixed duopoly game model with market share preference[J]. Chaos:An Interdisciplinary Journal of Nonlinear Science,2018,28(2):023101.
[7] ASKAR S S. On complex dynamics of Cournot-Bertrand game with asymmetric market information[J].Applied Mathematics and Computation,2021,393:125823.
[8] MATSUMURA T,OGAWA A. Price versus quantity in a mixed duopoly[J]. Economics Letters,2012,116(2):174-177.
[9] NAKAMURA Y. Price versus quantity in a mixed duopoly:The case of relative profit maximization[J].Economic Modelling,2015,44:37-43.
[10] ASKAR S S. Nonlinear dynamic investigations and global analysis of a Cournot duopoly game with two different objectives[J]. Chaos,Solitons and Fractals,2022,155:111711.
[11] NAIMZADA A K,TRAMONTANA F. Dynamic properties of a Cournot-Bertrand duopoly game with differentiated products[J]. Economic Modelling,2012,29(4):1436-1439.
[12] AGIZA H N,ELSADANY A A. Chaotic dynamics in nonlinear duopo ly game with heterogeneous players[J]. Applied Mathematics and Computation,2004,149(3):843-860.
[13] AHMED E,AGIZA H N,HASSAN S Z. On modifications of Puu’s dynamical duopoly[J]. Chaos,Solitons&Fractals,2000,11(7):1025-1028.
[14] PENG Y,XIAO Y,LU Q,et al. Chaotic dynamics in Cournot duopoly model with bounded rationality based on relative profit delegation maximization[J]. Physica A:Statistical Mechanics and its Applications,2020,560:125174.
基本信息:
DOI：
中图分类号:O225;F272
引用信息:
[1]焦琳致,包振华.混合双寡头Bertrand博弈模型的复杂动态性研究[J].汕头大学学报(自然科学版),2025,40(01):72-80.
基金信息:
辽宁省教育厅基本科研项目（JYTMS20231043）