A Dynamic Stackelberg–Cournot Duopoly Model with Heterogeneous Strategies through One-Way Spillovers
Joint Authors
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-10-16
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
Many works studied on complex dynamics of Cournot or Stackelberg games, but few references discussed a dynamic game model combined with the Cournot game phase and Stackelberg game phase.
Under the assumption that R&D spillovers only flow from the R&D leader to the R&D follower, a duopoly Stackelberg–Cournot game with heterogeneous expectations is considered in this paper.
Two firms with different R&D capabilities determine their R&D investments sequentially in the Stackelberg R&D phase and make output decisions simultaneously in the Cournot production phase.
R&D spillovers, R&D investments, and technological innovation efficiency are introduced in our model.
We find that: (i) the boundary equilibrium of the dynamic Stackelberg–Cournot duopoly system, where two players adopt boundedly rational expectation and naïve expectation, respectively, is unstable if the Nash equilibrium of the system is strictly positive.
(ii) The Nash equilibrium of the dynamic Stackelberg–Cournot duopoly system, where two players adopt boundedly rational expectation and naïve expectation, respectively, is locally asymptotically stable only if the model parameters meet certain conditions.
Especially, results indicate that small value of R&D spillovers or big value of output adjustment speed may yield bifurcations or even chaos.
Numerical simulations are performed to exhibit maximum Lyapunov exponents, bifurcation diagrams, strange attractors, and sensitive dependence on initial conditions to verify our findings.
It is also shown that the chaotic behaviors can be controlled with the state variables feedback and parameter variation method.
American Psychological Association (APA)
Long, Jianjun& Huang, Hui. 2020. A Dynamic Stackelberg–Cournot Duopoly Model with Heterogeneous Strategies through One-Way Spillovers. Discrete Dynamics in Nature and Society،Vol. 2020, no. 2020, pp.1-11.
https://search.emarefa.net/detail/BIM-1152970
Modern Language Association (MLA)
Long, Jianjun& Huang, Hui. A Dynamic Stackelberg–Cournot Duopoly Model with Heterogeneous Strategies through One-Way Spillovers. Discrete Dynamics in Nature and Society No. 2020 (2020), pp.1-11.
https://search.emarefa.net/detail/BIM-1152970
American Medical Association (AMA)
Long, Jianjun& Huang, Hui. A Dynamic Stackelberg–Cournot Duopoly Model with Heterogeneous Strategies through One-Way Spillovers. Discrete Dynamics in Nature and Society. 2020. Vol. 2020, no. 2020, pp.1-11.
https://search.emarefa.net/detail/BIM-1152970
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1152970