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The two‐dimensional flow field is numerically investigated using a compact finite difference and a pseudo‐spectral method when two fluids with different physical properties are mixing under gravity as well as flow rate. The gravity and the viscous mobility affect the fingering instability, i.e. the mixing range shrinks much at the large viscous mobility or the strong gravity. When the gravitation acts parallel to the main stream, the flow decelerates or accelerates according to its direction. The fingertip velocity is exactly expressed by a pure cosine function and especially invariant when the gravity acts along the −y direction at the high Peclet number. The maximum and fingertip velocities at the very low Peclet number are nearly symmetric with respect to the −y direction perpendicular to the main flow direction x. When the gravity acts along the −y direction, the flow field shows the asymmetry, and a pair of vortices is generated at both the very high Peclet number and less viscous mobility number. As the viscous mobility becomes large, the vortex scale enlarges at the small Peclet number, while the vortices are slightly destroyed at the relatively high Peclet number. As the gravitational angle changes clockwise from downstream to upstream, a pair of vortices evolves through a process of asymmetry.

Previous scholars have assumed that multinational enterprises (MNEs) can reduce the liability of foreignness and increase profitability by investing in corporate social responsibility (CSR). However, empirical validation of this assumption has rarely been attempted. This study aims to provide empirical evidence that the adoption of multi-stakeholder initiatives, which are globally recognized as signals of CSR, helps MNEs increase profits from internationalization.

Fixed effect models, which address model misspecification problems, and instrumental variable estimation, which controls for the endogeneity in firms’ choice of internationalization, offer empirical evidence supporting the moderating effects of global multi-stakeholder initiatives on the relationship between internationalization and firm performance.

This study examines the moderating role of multi-stakeholder initiatives in the relationship between internationalization and firm performance, drawing on signaling and stakeholder theories. The results suggest that the signaling effect of multi-stakeholder initiatives can help MNEs overcome the liability of foreignness and, therefore, profit from overseas markets.

Although the internationalization–firm performance relationship has been a subject of debate in the field of international business, the role of firms’ stakeholder engagement in this relationship has been largely overlooked in previous studies. In this study, the authors explore the impact of multi-stakeholder initiatives on the internationalization–firm performance relationship. Our primary contention is that multi-stakeholder initiatives have moderating effects on this relationship by reducing the liability of foreignness experienced by MNEs in host countries. Furthermore, the findings suggest that active engagement in multi-stakeholder initiatives significantly contributes to the financial success of MNEs as they internationalize.