A large proportion of recent studies on cooperative Multi-Agent Reinforcement Learning (MARL) focus on the policy-learning process in scenarios with stationary opponents (or without opponents). This paper, instead, investigates a different challenge of achieving team superiority in dynamic competitions among competitors that evolve dynamically with MARL. We aim to enhance the competitiveness of such MARL learners by enabling them to adjust their own learning settings dynamically, so as to take quick counter-measures against the policy shift of competitor learners, or to learn faster to suppress the opponents. We propose a Competitive Auto-Multiagent Learner with Fuzzy Feedback (CALF) with two essential highlights: (1) CALF establishes feedback controllers to achieve real-time adjustments based on fuzzy logic, using human-readable fuzzy rules to provide significant explainability and flexibility; (2) CALF integrates Bayesian Optimization to search and optimize the feedback fuzzy logic rules automatically. CALF can be used to apply real-time adjustments for MARL hyperparameters and intrinsic rewards. We also give solid empirical results to show that CALF significantly promotes team competitiveness in adversarial competitions, spanning from small-scale tasks involving 2 teams to large-scale tasks involving 3 teams and hundreds of agents. Furthermore, CALF exhibits superior competitiveness when engaging in competition with established competitors like Qmix, Qtran, and Qplex in dynamic competitive environments. Moreover, the experiments also demonstrate that the integration of the fuzzy logic with Bayesian Optimization offers considerable transferability and explainability, enabling a CALF-implemented learner optimized from one scenario to be transferred to other distinct scenarios.