关键词: 非合作博弈, 解雇机制, 最优投资, HJB方程

Abstract: Information asymmetry, which leads to managers to manipulate corporate performance, adopt risky investment strategies, and focus too much on short-term interests, has been a major concern in academia. It also has an impact on the incentive compatibility of the contracts between shareholders and managers of a firm. In order to mitigate the agency conflicts, shareholders will design a series of mechanisms to motivate managers to choose a more suitable strategy for the development of the enterprise. The dismissal of the CEO for his poor performance is an important measure taken by the board. Since it not only results in the loss of dedicated human capital invested in the previous period, but also affects the managers’ perks, professional reputations, and even future employments, managers have strong incentives to avoid dismissal.
Several scholars have examined performance and non-performance factors affecting the dismissal of managers, indirectly suggesting that executive turnover has become a common phenomenon. However, because it is important to maintain policy continuity and consistency in corporate management, and the arrival of the successor may indicate changes in corporate future decisions: either correcting past mistakes or introducing policies reflecting the different views of the new manager.This releases different signals to investors and affects the market environment. Moreover, when managers anticipate their imminent dismissal, they are more likely to have “short-sighted biases” and place more emphases on short-term performances at the expense of projects that create long-term value for the firm, resulting in higher agency costs. Therefore, combined with the firm’s actual situation, analyzing the impact of executive dismissal on other decisions and corporate future development is significant in evaluating its effectiveness.
Based on the current research results, this paper describes the firm’s capital accumulation process from different perspectives, and introduces the dismissal mechanism on the basis of shareholders hiring a professional manager responsible for project investment. Aiming at the problem of non-cooperation between shareholders and the project manager in the presence of dismissal threat, we construct two-stage differential game models in a continuous time. The Nash equilibrium solutions of the game, which is the optimal efforts of the manager and shareholders, are obtained through the HJB equations and the optimal investment decision of the manager is solved by using the backward induction method. Besides, we discuss the influence of the dismissal mechanism on the above results and verify them by means of numerical simulations.
Our contributions are threefold. First, this paper describes the firm’s capital accumulation process from different perspectives. It takes into account both physical capital in the form of plants, equipment and also includes non-physical capital such as knowledge, skills, etc., which plays an important role in the development of modern enterprises. Second, when exploring the incentive role of dismissal for managers, this paper considers the attributes of the enterprise in production, operation and management, theoretically proving that the threat of dismissal will make managers put more efforts in the first period of the two-phase project under certain conditions. Third, considering the heterogeneity of enterprises in terms of the proportion of physical capital, management methods and investment strategies, this study provides reference for shareholders’ reasonable dismissal decisions and managers’ investment strategies.
The results of the study show that: (1)In the case where the enterprise parameter settings satisfy a certain condition, when the proportion of physical capital is greater than a threshold, the manager will choose a higher optimal investment ratio with the increase in initial capital, but the increase in dismissal probability will inhibit the enthusiasm of the manager for investing in the project; on the contrary, when the proportion of firm’s physical capital is less than the threshold, the increase in initial capital will have a negative impact on the optimal investment ratio, but with the rise in dismissal risk, the manager will invest more. (2)The reinvestment that the manager chooses will gradually decrease with the increasing proportion of physical capital in a certain range. (3)There is a positive correlation between the manager’s optimal effort in the first stage and the dismissal probability, which is unrelated to the share of the firm’s physical capital, so the dismissal mechanism can effectively motivate managers to work hard.
The follow-up study will attempt to relax the constraints on the relevant parameters and take into account the interactions between other variables and the probability of dismissal. Moreover, both incorporating the probability of dismissal as an endogenous variable in the model, and exploring the mechanism of dismissal’s effect on managers’ investment strategies as well as optimal efforts need further research.

Key words: non-cooperative game, dismissal mechanism, optimal investment, HJB equation