In this paper we develop a game theoretic learning framework for deep generative models. Firstly, the problem of minimizing the dissimilarity between the generator distribution and real data is introduced based on f-divergence. Secondly, the optimization problem is transformed into a zero-sum game with two adversarial players, and the existence of Nash equilibrium is established in the quasi-concave-convex case under suitable conditions. Thirdly, a general Bregman-based learning algorithm is proposed to find the Nash equilibria. The algorithm is proved to have a doubly logarithmic convergence time with respect to the precision of the minimax value in potential convex games. Lastly, our methodology is implemented in three application scenarios and compared with several existing optimization algorithms. Both qualitative and quantitative evaluation show that the generative model trained by our algorithm has the state-of-art performance.