In this paper, a novel approach is presented to mitigate the issue of domain shift observed in big-data classification. Since little information is available about the shift, we introduce a "distortion model", and obtain additional data-samples to represent the shift. Next, a deep neural network (DNN), referred as "classifier," is used to compensate for the shift by learning through these additional samples while maintaining performance on training samples. As the exact magnitude of domain shift is uncertain, we compensate for the optimal expected shift by formulating a zero-sum game. In the proposed game, the distortion model is viewed as the maximizing player which increases the domain shift while the classifier becomes the minimizing player that reduces the impact of domain shift on learning. The Nash solution of the game, which is demonstrated mathematically, provides the domain shift and its optimal adaptation through the classifier. To solve the proposed game for the Nash solution, a direct error-driven learning scheme is introduced where a cost function is derived and solved for each layer in the DNN and the distortion model. Comprehensive mathematical and simulation study is presented to demonstrate the efficacy of the approach.