Stability, Global Dynamics, and Social Welfare of a Two-Stage Game under R&D Spillovers

In this paper, a repeated two-stage oligopoly game where two boundedly rational firms produce homogeneous product and apply gradient adjustment mechanism to decide their individual R&D investment is considered. Results concerning the equilibrium in the built model and the stability are discussed...

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Bibliographic Details
Published in:Mathematical problems in engineering 2021, Vol.2021, p.1-19
Main Authors: Zhou, Wei, Chu, Tong, Wang, Xiao-Xue
Format: Article
Language:English
Subjects:
Adjustment
Behavior
Bifurcations
Competition
Competitive advantage
Cooperation
Costs
Decision making
Dynamic stability
Game theory
Games
Oligarchy
Organization theory
Product differentiation
Profits
R&D
Research & development
Stability analysis
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Summary:In this paper, a repeated two-stage oligopoly game where two boundedly rational firms produce homogeneous product and apply gradient adjustment mechanism to decide their individual R&D investment is considered. Results concerning the equilibrium in the built model and the stability are discussed. The effects of system parameters on the complex dynamical behaviors of the built game are analyzed. We find that the system can lose stability through a flip bifurcation or a Neimark–Sacker bifurcation. In addition, the coexistence of multiattractors is also discussed using the so-called basin of attraction. At the end of this research, the social welfare of the given duopoly game is also studied.
ISSN:1024-123X
1563-5147
DOI:10.1155/2021/2096868