Analyzing the Relationship between Supervisors and Post-Graduates Based on Differential Game Theory

A healthy relationship between supervisors and postgraduates is critical for their academic achievements and personal development. This paper quantitatively discusses such a relationship from the viewpoint of differential game theory. First, a mathematic model was established to describe the evolutionary dynamics of the academic level of the supervisor-postgraduate community, which is related to the two parties' positive and negative efforts. Then, the objective function aimed at maximizing the individual and total benefit of the community was constructed. After that, the differential game relationships in the non-cooperative, cooperative and Stackelberg scenarios were formulated and solved. A comparison of the three game scenarios showed that the optimal academic level and total benefit of the community were 22% higher in the cooperative scenario than in the non-cooperative and Stackelberg game scenarios. Moreover, the influence of model parameters on the game results was analyzed. The results indicate that, for the supervisor-led Stackelberg game, when the sharing cost ratio is increased to a specific level, the supervisor's optimal benefit will not be further improved.