In this work, we present a multi-agent learning model based on the maximum entropy (MAXEnt) and the rate distortion function to define, respectively, the environment of the agents and their understanding about it. The avoidance of redundant information under distortion conditions is used to define a distortion-based potential function that is minimized in order to find an equilibrium point in a potential game setting, in which the Lagrange multiplier β, used as input in the Blahut-Arimoto algorithm, determines the rationality in the learning process. The model performance is evaluated in a secondary voltage controller in order to achieve reactive power sharing between distributed generators (DGs) in a micro-grid. Simulation results demonstrate a good response in terms of reactive power distribution when the load is increased in a DG without considerable affectations in the voltage stability.