| 91 | 0 | 61 |
| 下载次数 | 被引频次 | 阅读次数 |
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.
Abstract：In this paper, a price game model is considered for mixed competition between state-owned enterprises and private enterprises, which produce a differentiated goods together,and determine the future price of the goods by using the principle of bounded rational expectation.A two-dimensional discrete dynamical system is established, and the boundary equilibrium point and Nash equilibrium point of the dynamical system are solved, and their stability is studied. In numerical analysis, the dynamics of the system are demonstrated through bifurcation diagram,maximum Lyapunov exponent, the strange attractor, and sensitive dependence on initial conditions.Finally, the state variables feedback and parameter variation can be used to control the chaos of the system, which makes the system ultimately stable.
[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.
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）