Global dynamics in a duopoly game with ESG penalty factors and corporate social responsibility

Yimeng He, Ningting Su, Yifan Zhu, Xiaole Yue and Zifei Lin

Chaos, Solitons & Fractals, 2026, vol. 210, issue P2

Abstract: This paper develops a nonlinear Cournot duopoly game model with quadratic costs. It incorporates Environmental, Social, and Governance (ESG) investment, Corporate Social Responsibility (CSR), and knowledge spillover effects. All these factors are integrated into a boundedly rational framework. We firstly take the background of green and sustainable development into account. It further investigates the impact of ESG investment on firms’ outputs, profits, and market evolution from both local and global nonlinear dynamic perspectives. The stability analysis of the proposed model is conducted, and the stable region of Nash equilibrium is given by the Jury criterion. The 2D-bifurcation diagrams show that the system has two different paths to chaos, the Flip and Neimark–Sacker bifurcations. Moreover, a multi-layer Arnold’s tongues structure is discovered near the Neimark–Sacker bifurcation. We find that higher ESG investment improves firm profitability but may also induce contact bifurcations and disconnected basins of attraction. In addition, multistability and contact bifurcations are detected through critical curves and basin evolution analysis, implying strong dependence of long-term market outcomes on initial conditions. Finally, a time-delay feedback control method is introduced, and the chaotic system can be stabilized to the Nash equilibrium when the feedback gain satisfies k>0.295. The study provides theoretical guidance for decision-makers to select appropriate adjustment strategies, ESG investment levels, and initial market decisions in order to maintain stable market competition and sustainable development.

Keywords: Global analysis; Duopoly game; ESG; Corporate social responsibility; Multistability (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:210:y:2026:i:p2:s0960077926008490

DOI: 10.1016/j.chaos.2026.118708

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