text: Summary ======== The authors present a new regularization term, inspired from game theory, which encourages the discriminator's gradient to have a norm equal to one. This leads to reduce the number of local minima, so that the behavior of the optimization scheme gets closer to the optimization of a zero-sum games with convex-concave functions. Clarity ====== Overall, the paper is clear and well-written. However, the authors should motivate better the regularization introduced in  section 2.3. Originality ========= The idea is novel and interesting. In addition, it is easy to implement it for any GANs since it requires only an additional regularization term. Moreover, the numerical experiments are in favor of the proposed method. Comments ========= - Why should the norm of the gradient should to be equal to 1 and not another value? Is this possible to improve the performance if we put an additional hyper-parameter instead? - Are the performances greatly impacted by other value of lambda and c (the suggested parameter values are lambda = c = 10)? - As mentioned in the paper, the regularization affects the modeling performance. Maybe the authors should add a comparison between different regularization parameters to illustrate the real impact of lambda and c on the performance. - GANs performance is usually worse on very big dataset such as Imagenet. Does this regularization trick makes their performance better?