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

Wei Zhou, Tong Chu and Xiao-Xue Wang

Mathematical Problems in Engineering, 2021, vol. 2021, 1-19

Abstract:

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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:2096868

DOI: 10.1155/2021/2096868

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