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Recent social networks' misinformation mitigation approaches tend to investigate how to reduce misinformation by considering a whole-network statistical scale. However, unbalanced misinformation exposures among individuals urge to study fair allocation of mitigation resources. Moreover, the network has random dynamics which change over time. Therefore, we introduce a stochastic and non-stationary knapsack problem, and we apply its resolution to mitigate misinformation in social network campaigns. We further propose a generic misinformation mitigation algorithm that is robust to different social networks' misinformation statistics, allowing a promising impact in real-world scenarios. A novel loss function ensures fair mitigation among users. We achieve fairness by intelligently allocating a mitigation incentivization budget to the knapsack, and optimizing the loss function. To this end, a team of Learning Automata (LA) drives the budget allocation. Each LA is associated with a user and learns to minimize its exposure to misinformation by performing a non-stationary and stochastic walk over its state space. Our results show how our LA-based method is robust and outperforms similar misinformation mitigation methods in how the mitigation is fairly influencing the network users.