Eigenvalues of the Jacobian matrix.

In the digital age, online public opinion plays a pivotal role in shaping social stability, policymaking, and public trust in institutions. Given the frequent occurrence of public opinion crises, it is imperative to explore their evolutionary dynamics and effective mitigation strategies. This study develops a three-party evolutionary game model involving the government, ordinary netizens, and media/KOLs, incorporating both inter-group strategy influence and intra-group incentive effects. The model enhances traditional replicator dynamics by embedding incentive coefficients that reflect the strategic suppressive or promotive effects within each group. Simulation results reveal that changes in incentive structures significantly affect the speed and stability of opinion convergence. For instance, when the media’s suppression of dissemination strategies is strong (), all groups reach near-equilibrium within 3–5 time steps, with netizen participation stabilizing above 0.99 by t = 3. However, when only the government’s suppressive influence increases (), convergence is slower and displays diminishing returns. As continues to rise, netizen responsiveness plateaus, indicating a saturation effect whereby excessive suppression loses effectiveness in accelerating stabilization. These findings challenge the assumption that earlier or stronger intervention is inherently more effective. Instead, they underscore the importance of calibrated timing and intensity, as public sentiment evolves through the interplay of government response, media coordination, and audience receptiveness. Netizens respond more rapidly than institutional actors, reflecting their sensitivity to perceived information gaps. Effective mitigation of negative sentiment thus requires not only timely action but also adaptive adjustment of strategic influence in accordance with systemic feedback.