PurposeThis study aims to disclose how the nature of corporate ownership, stock efficiency and wage level affect the optimal proportion of employee stock.Design/methodology/approachThis paper studies three duopoly markets: two private enterprises, two state-owned enterprises (SOEs) and a private enterprise and an SOE. The competitions between the two parties are taken as a two-stage dynamic sequential game and studied through back-induction.FindingsThe results reveal that the enterprise ownership has a directly bearing on the optimal proportion of employee stock and determines whether to implement the employee stock ownership plan (ESOP) and the specific level of the plan. The optimal proportion of employee stock is positively correlated with its contribution to enterprise efficiency. There are many influencing factors on the effect of wage level on the optimal proportion of employee stock, namely, the ownership nature of ESOP implementer and efficiency difference of different nature stocks.Social implicationsThe results of this study provide policy recommendations for companies preparing to implement ESOP.Originality/valueThe research findings provide policy implications for enterprises to prepare a suitable ESOP and the reform of national equities, especially the mixed-ownership reform in China.

Boundary or interior layer problems of high-dimensional convection–diffusion equations have distinct asymmetry. Consequently, computational grid distributions and linear algebraic systems arising from finite difference schemes for them are also asymmetric. Numerical solutions for these kinds of problems are more complicated than those symmetric problems. In this paper, we extended our previous work on the partial semi-coarsening multigrid method combined with the high-order compact (HOC) difference scheme for solving the two-dimensional (2D) convection–diffusion problems on non-uniform grids to the three-dimensional (3D) cases. The main merit of the present method is that the multigrid method on non-uniform grids can be performed with a different number of grids in different coordinate axes, which is more efficient than the multigrid method on non-uniform grids with the same number of grids in different coordinate axes. Numerical experiments are carried out to validate the accuracy and efficiency of the present method. It is shown that, without losing the high precision, the present method is very effective to reduce computing cost by cutting down the number of grids in the direction(s) which does/do not contain boundary or interior layer(s).