One of the fundamental problems of an interconnected interactive system is the huge amounts of data that are being generated by every entity. Unfortunately, what we seek is not data but information, and therefore, a growing bottleneck is exactly how to extract and learn useful information from data. In this paper, the information-Theoretic learning in data-driven games is studied. This learning shows that the imitative Boltzmann-Gibbs strategy is the maximizer of the perturbed payoff where the perturbation function is the relative entropy from the previous strategy to the current one. In particular, the imitative strategy is the best learning scheme with the respect to data-driven games with cost of moves. Based on it, the classical imitative Boltzmann-Gibbs learning in data-driven games is revisited. Due to communication complexity and noisy data measurements, the classical imitative Boltzmann-Gibbs cannot be applied directly in situations were only numerical values of player's own payoff is measured. A combined fully distributed payoff and strategy imitative learning (CODIPAS) is proposed. Connections between the rest points of the resulting game dynamics, equilibria are established.