Coverage-guided gray-box fuzzing (CGF) is an efficient software testing technique. There are usually multiple objectives to optimize in CGF. However, existing CGF methods cannot successfully find the optimal values for multiple objectives simultaneously. In this paper, we propose a gray-box fuzzer for multi-objective optimization (MOO) called MobFuzz. We model the multi-objective optimization process as a multiplayer multi-armed bandit (MPMAB). First, it adaptively selects the objective combination that contains the most appropriate objectives for the current situation. Second, our model deals with the power schedule, which adaptively allocates energy to the seeds under the chosen objective combination. In MobFuzz, we propose an evolutionary algorithm called NIC to optimize our chosen objectives simultaneously without incurring additional performance overhead. To prove the effectiveness of MobFuzz, we conduct experiments on 12 real-world programs and the MAGMA data set. Experiment results show that multi-objective optimization in MobFuzz outperforms single-objective fuzzing in the baseline fuzzers. In contrast to them, MobFuzz can select the optimal objective combination and increase the values of multiple objectives up to 107%, with at most a 55% reduction in the energy consumption. Moreover, MobFuzz has up to 6% more program coverage and finds 3x more unique bugs than the baseline fuzzers. The NIC algorithm has at least a 2x improvement with a performance overhead of approximately 3%.