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

Wei Zhou | Zendy; Tong Chu | Zendy; Xiaoxue Wang | Zendy

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

Author(s) -

Wei Zhou,

Tong Chu,

Xiaoxue Wang

Publication year - 2021

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2021/2096868

Subject(s) - duopoly , economics , oligopoly , mathematical economics , stability (learning theory) , microeconomics , repeated game , bifurcation , welfare , social welfare , investment (military) , game theory , mathematics , computer science , cournot competition , nonlinear system , physics , market economy , quantum mechanics , machine learning , politics , political science , law

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.

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