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Complex dynamics and control of a dynamic R&D Bertrand triopoly game model with bounded rational rule

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Abstract

In this study, we model a dynamic R&D two-stage input competition triopoly game characterized by players with a bounded rationality rule as a discrete nonlinear dynamic system, where we focus on spillover effects on cost reductions. We analyze the stability of the Nash equilibrium and obtain the stability conditions and the stability region. We show that the Nash equilibrium loses its stability and complex dynamic behaviors occur after increasing the input adjustment speed parameters. Finally, the straight-line stabilization method is applied for chaos control. The results obtained have theoretical implications for manufacturers regarding R&D input decisions in real economic markets.

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Acknowledgements

We would like to thank the reviewers for their valuable comments and suggestions. The research was supported by the National Natural Science Foundation of China (Grant No. 61273231); it was also supported by the Fundamental Research Funds for the Central Universities (Grant No. 2014QNB08), Postdoctoral Fund of Jiangsu Province (Grant No. 1401055B) and Department of Education and Social Sciences project of Jiangsu Provincial (Grant No. 2014SJD413).

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Authors and Affiliations

  1. School of Management, China University of Mining and Technology, Xuzhou, 221116, China

    Hongliang Tu & Xinyu Wang

  2. School of Information and Management, Jiangxi University of Finance and Economics, Nanchang, 330013, China

    Hongliang Tu

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  1. Hongliang Tu
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  2. Xinyu Wang
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Correspondence to Xinyu Wang.

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Tu, H., Wang, X. Complex dynamics and control of a dynamic R&D Bertrand triopoly game model with bounded rational rule. Nonlinear Dyn 88, 703–714 (2017). https://doi.org/10.1007/s11071-016-3271-6

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