Analysis of heterogeneous duopoly game with information asymmetry based on extrapolative mechanism

Jing Yuan; Jianjun Zhu

doi:10.1515/snde-2022-0052

Abstract

Information plays an important role in decision-making process in oligopoly market. This paper establishes two Cournot duopoly games with information asymmetry based on extrapolative mechanism, and focus on the impacts of information asymmetry from the perspective of stability, complexity and profit. The results show that the extrapolative mechanism plays a different role for heterogeneous expectation firms. In general, proper prediction of rival’s output information is conducive to the improvement of firms’ profit and system stability. However, for firms adopting the adaptive adjustment mechanism, the optimal profit does not occur for the most perfect prediction. Firms who adopt gradient adjustment mechanism are worth to improve prediction accuracy to promote the system stability and the profit. In addition, it is more important for all firms to control their own output adjustment mechanism to gain more profits.

Keywords: bounded rationality; duopoly game; heterogeneous expectations; information asymmetry; nonlinear dynamics

Corresponding author: Jing Yuan, College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, China; College of Management Science and Engineering, Anhui University of Technology, Maanshan, China; and Key Laboratory of Multidisciplinary Management and Control of Complex Systems of Anhui Higher Education Institute, Maanshan, China, E-mail: yuanjing903@163.com

Funding source: National Natural Science Foundation of China

Award Identifier / Grant number: 72071106

Award Identifier / Grant number: 72074001

Funding source: The Open Fund of Key Laboratory of Anhui Higher Education Institute

Award Identifier / Grant number: RZ 2200000691

Funding source: The Research Foundation for the Youth Scholars of Anhui University of Technology

Award Identifier / Grant number: No. RD19100287

Acknowledgment

The authors would like to thank the reviewer for the valuable and constructive comments which improved the paper. The research of J. Yuan was partially supported by the Open Fund of Key Laboratory of Anhui Higher Education Institute (No. RZ2200000691) and the Research Foundation for the Youth Scholars of Anhui University of Technology (No. RD19100287). The research of J.J. Zhu was partially supported by the National Natural Science Foundation of China under Grant (No. 72071106, 72074001).

Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: This work was supported by the National Natural Science Foundation of China under Grant (No. 72071106, 72074001), the Open Fund of Key Laboratory of Anhui Higher Education Institute (No. RZ2200000691) and the Research Foundation for the Youth Scholars of Anhui University of Technology (No. RD19100287).
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

References

Agiza, H. N., and A. A. Elsadany. 2003. “Nonlinear Dynamics in the Cournot Duopoly Game with Heterogeneous Players.” Physica A 320: 512–24. https://doi.org/10.1016/s0378-4371(02)01648-5.Search in Google Scholar

Askar, S. S. 2021. “On Complex Dynamics of Cournot-Bertrand Game with Asymmetric Market Information.” Applied Mathematics and Computation 393 (3): 125823. https://doi.org/10.1016/j.amc.2020.125823.Search in Google Scholar

Askar, S. S., A. Ibrahim, and A. A. Elsadany. 2021. “Dynamics of a Heterogeneous Constraint Profit Maximization Duopoly Model Based on an Isoelastic Demand.” Complexity 2021: 6687544, https://doi.org/10.1155/2021/6687544.Search in Google Scholar

Bacchiocchi, A., G. I. Bischi, and G. Giombini. 2022. “Non-Performing Loans, Expectations and Banking Stability: A Dynamic Model.” Chaos, Solitons & Fractals 157: 111906. https://doi.org/10.1016/j.chaos.2022.111906.Search in Google Scholar

Bischi, G. I., and A. Naimzada. 2000. “Global Analysis of a Dynamic Duopoly Game with Bounded Rationality.” In Advances in Dynamic Games and Applications, 361–85. Berlin: Springer.10.1007/978-1-4612-1336-9_20Search in Google Scholar

Bischi, G. I., and M. Kopel. 2001. “Equilibrium Selection in a Nonlinear Duopoly Game with Adaptive Expectations.” Journal of Economic Behavior & Organization 46 (1): 73–100. https://doi.org/10.1016/s0167-2681(01)00188-3.Search in Google Scholar

Chen, J., H. Pun, and Q. Zhang. 2023. “Eliminate Demand Information Disadvantage in a Supplier Encroachment Supply Chain with Information Acquisition.” European Journal of Operational Research 305 (2): 659–73. https://doi.org/10.1016/j.ejor.2022.06.002.Search in Google Scholar

Culda, L. C., E. Kaslik, and M. Neamţu. 2022. “Stability and Bifurcations in a General Cournot Duopoly Model with Distributed Time Delays.” Chaos, Solitons & Fractals 162: 112424. https://doi.org/10.1016/j.chaos.2022.112424.Search in Google Scholar

Dubiel-Teleszynski, T. 2011. “Nonlinear Dynamics in a Heterogeneous Duopoly Game with Adjusting Players and Diseconomies of Scale.” Communications in Nonlinear Science and Numerical Simulation 16 (1): 296–308. https://doi.org/10.1016/j.cnsns.2010.03.002.Search in Google Scholar

Elsadany, A. A. 2017. “Dynamics of a Cournot Duopoly Game with Bounded Rationality Based on Relative Profit Maximization.” Applied Mathematics and Computation 294: 253–63. https://doi.org/10.1016/j.amc.2016.09.018.Search in Google Scholar

Fischer, C., and H. Normann. 2019. “Collusion and Bargaining in Asymmetric Cournot Duopoly-An Experiment.” European Economic Review 111: 360–79. https://doi.org/10.1016/j.euroecorev.2018.10.005.Search in Google Scholar

Garcia-Perez, L., J. Grau-Climent, R. Alonso-Sanz, and J. C. Losada. 2022. “Complex Dynamics of a Cournot Quantum Duopoly Game with Memory and Heterogeneous Players.” Entropy 24 (10): 1333. https://doi.org/10.3390/e24101333.Search in Google Scholar PubMed PubMed Central

Gao, X., W. J. Zhong, and S. E. Mei. 2012. “Equilibrium Stability of a Nonlinear Heterogeneous Duopoly Game with Extrapolative Foresight.” Mathematics and Computers in Simulation 82 (11): 2069–78. https://doi.org/10.1016/j.matcom.2012.04.006.Search in Google Scholar

Guo, Z. B., and J. H. Ma. 2016. “The Influence of Information Acquisition on the Complex Dynamics of Market Competition.” International Journal of Bifurcation and Chaos 26 (1): 1650008. https://doi.org/10.1142/s0218127416500085.Search in Google Scholar

Guo, Z. B. 2019. “Complexity and Implications on Channel Conflict under the Uncertain Impacts of Online Customer Reviews.” Nonlinear Dynamics 96 (3): 1971–87. https://doi.org/10.1007/s11071-019-04898-7.Search in Google Scholar

Hamid, G., A. O. Driss, E. A. Mohamed, B. Mohamed, and J. Mostafa. 2020. “Analysis of a Dynamics Duopoly Game with Two Content Providers.” Chaos, Solitons & Fractals 131: 109466. https://doi.org/10.1016/j.chaos.2019.109466.Search in Google Scholar

Hu, S. S. 2001. Principle of Automatic Control, 321–30. Beijing: Science Press.Search in Google Scholar

Liu, Y. F., and M. Sun. 2020. “Application of Duopoly Multi-Periodical Game with Bounded Rationality in Power Supply Market Based on Information Asymmetry.” Applied Mathematical Modelling 87: 300–16. https://doi.org/10.1016/j.apm.2020.06.007.Search in Google Scholar

Long, J. J., and H. Huang. 2022. “Stability of Equilibrium Production-Price in a Dynamic Duopoly Cournot-Bertrand Game with Asymmetric Information and Cluster Spillovers.” Mathematical Biosciences and Engineering 19 (12): 14056–73. https://doi.org/10.3934/mbe.2022654.Search in Google Scholar PubMed

Ma, J. H., and Y. Hong. 2021. “Dynamic Game Analysis on Pricing and Service Strategy in a Retailer-Led Supply Chain with Risk Attitudes and Free-Ride Effect.” Kybernetes 51 (3): 1199–230. https://doi.org/10.1108/k-07-2020-0459.Search in Google Scholar

Mai, F. X., J. X. Zhang, and X. J. Sun. 2021. “Dynamic Analysis of Pricing Model in a Book Supply Chain.” International Journal of Production Economics 233: 108026. https://doi.org/10.1016/j.ijpe.2021.108026.Search in Google Scholar

Ni, J., J. Zhao, and L. K. Chu. 2021. “Supply Contracting and Process Innovation in a Dynamic Supply Chain with Information Asymmetry.” European Journal of Operational Research 288 (2): 552–62. https://doi.org/10.1016/j.ejor.2020.06.008.Search in Google Scholar

Puu, T. 1996. “Complex Dynamics with Three Oligopolists.” Chaos, Solitons & Fractals 12: 2075–81. https://doi.org/10.1016/s0960-0779(96)00073-2.Search in Google Scholar

Puu, T. 2000. Attractors, Bifurcation and Chaos: Nonlinear Phenomena in Economics. Berlin: Springer.10.1007/978-3-662-04094-2Search in Google Scholar

Rofin, T. M., and M. Biswajit. 2018. “Impact of Price Adjustment Speed on the Stability of Bertrand–Nash Equilibrium and Profit of the Retailers.” Kybernetes 47 (8): 1494–523. https://doi.org/10.1108/k-08-2017-0301.Search in Google Scholar

Song, Q. Q., W. L. Zhang, Y. R. Jiang, and J. Geng. 2022. “The Effect of Price Discrimination on Dynamic Duopoly Games with Bounded Rationality.” Studies in Nonlinear Dynamics & Econometrics 26 (2): 287–311. https://doi.org/10.1515/snde-2019-0137.Search in Google Scholar

Tian, Y., J. H. Ma, L. Xie, T. Koivumäki, and V. Seppänen. 2020. “Coordination and Control of Multi-Channel Supply Chain Driven by Consumers’ Channel Preference and Sales Effort.” Chaos, Solitons & Fractals 132: 109576. https://doi.org/10.1016/j.chaos.2019.109576.Search in Google Scholar

Ueda, M. 2019. “Effect of Information Asymmetry in Cournot Duopoly Game with Bounded Rationality.” Applied Mathematics and Computation 362: 124535. https://doi.org/10.1016/j.amc.2019.06.049.Search in Google Scholar

Wang, Y., and X. Wang. 2010. Dynamic Analysis of Economic Systems, 2–10. Beijing: China Machine Press.Search in Google Scholar

Xu, H. Y., X. M. Liu, and H. Huang. 2023. “Information Sharing and Order Allocation Rule in Dual-Sourcing.” Omega 114: 102741. https://doi.org/10.1016/j.omega.2022.102741.Search in Google Scholar

Yu, W. S., and Y. Yu. 2018. “The Stability of Bayesian Nash Equilibrium of Dynamic Cournot Duopoly Model with Asymmetric Information.” Communications in Nonlinear Science and Numerical Simulation 63: 101–16. https://doi.org/10.1016/j.cnsns.2018.03.001.Search in Google Scholar

Yu, Y. 2016. “Emission Policy Simulation and System Dynamics Research-Based on Dynamic Game Perspective.” China Population, Resources and Environment 26: 119–27.Search in Google Scholar

Yan, R. 2010. “Demand Forecast Information Sharing in the Competitive Online and Traditional Retailers.” Journal of Retailing and Consumer Services 17 (5): 386–94. https://doi.org/10.1016/j.jretconser.2010.03.019.Search in Google Scholar

Zhang, Y. F., and X. Gao. 2019. “Equilibrium Selection of a Homogenous Duopoly with Extrapolative Foresight.” Communications in Nonlinear Science and Numerical Simulation 67: 366–74. https://doi.org/10.1016/j.cnsns.2018.07.028.Search in Google Scholar

Zhao, L. W., J. G. Du, and Q. W. Wang. 2019. “Nonlinear Analysis and Chaos Control of the Complex Dynamics of Multi-Market Cournot Game with Bounded Rationality.” Mathematics and Computers in Simulation 162: 45–57. https://doi.org/10.1016/j.matcom.2019.01.004.Search in Google Scholar

Zhou, D., J. X. Pi, G. H. Yang, and H. Yang. 2022. “Nonlinear Dynamics of a Heterogeneous Quantum Commons’ Tragedy.” Physica A 608: 128231. https://doi.org/10.1016/j.physa.2022.128231.Search in Google Scholar

Supplementary Material

This article contains supplementary material (https://doi.org/10.1515/snde-2022-0052).

Received: 2022-06-14

Accepted: 2023-02-07

Published Online: 2023-03-06

You are currently not able to access this content.

Supplementary Material Details