Prolonged periods of cognitive workload will cause mental fatigue, but objective, quantitative, and sensitive measurements that reflect long-term, stress-induced mental fatigue have yet to be elucidated. This study aims to apply a potential marker of Rényi entropy to investigate the mental fatigue changes in a long-term, high-level stress condition and compare three different instruments for assessment of mental fatigue: EEG, the oddball task, and self-scoring. We recruited nine individuals who participated in a 5-day intellectually challenging competition. The participants were assessed for mental fatigue each day of the competition using prefrontal cortex electroencephalogram (EEG). Reaction time in an oddball task and self-rated scoring were used comparatively to evaluate the performance of the EEG. Repeated measures ANOVA was utilized to analyze the differences among score, reaction time, and wavelet Rényi entropy. The results demonstrated that both wavelet Rényi entropy extracted from EEG and self-rated scoring revealed significant increases in mental fatigue during the 5 days of competition (P < 0.001). The reaction time of the oddball task did not show significant changes during the five-day competition (P = 0.066). Moreover, the wavelet Rényi entropy analysis of EEG showed greater sensitivity than the self-rated scoring and reaction time of the oddball task for measuring mental fatigue changes. In conclusion, this study shows that mental fatigue accumulates during long-term, high-level stress situations. The study also indicates that EEG wavelet Rényi entropy is an efficient metric to reflect the change of mental fatigue under a long-term stress condition and that EEG is a better method to assess long-term mental fatigue.