Research on quality management of higher education from the perspective of the evolutionary game

Graduate education expansion in China brings quality management challenges, yet existing research predominantly employs static frameworks analyzing bilateral relationships, neglecting dynamic multi-stakeholder interactions and evolutionary mechanisms. We develop a tripartite evolutionary game model incorporating supervisors, students, and college administrations to examine how strategic choices evolve toward stable equilibria under bounded rationality. Through replicator dynamics analysis, Jacobian stability assessment, and numerical simulation, we identify five equilibrium scenarios including mutual disengagement, unilateral free-riding, and optimal cooperation. Results show that high-quality equilibria emerge when complementarity conditions are satisfied where net returns to serious effort exceed free-riding benefits for both supervisors and students, while administrative gains from strict oversight justify intervention costs. Sensitivity analysis reveals equilibrium structures depend on inequality constraint satisfaction rather than precise parameter values. Stochastic extensions demonstrate systems exhibit persistent fluctuations around deterministic states due to environmental uncertainties. Findings suggest sustainable quality improvement requires coordinated restructuring of incentive systems through reward calibration, cost reduction, and complementarity enhancement rather than intensified monitoring alone.