We propose studying GAN training dynamics as regret minimization, which is in contrast to the popular view that there is consistent minimization of a divergence between real and generated distributions. We analyze the convergence of GAN training from this new point of view to understand why mode collapse happens. We hypothesize the existence of undesirable local equilibria in this non-convex game to be responsible for mode collapse. We observe that these local equilibria often exhibit sharp gradients of the discriminator function around some real data points. We demonstrate that these degenerate local equilibria can be avoided with a gradient penalty scheme called DRAGAN. We show that DRAGAN enables faster training, achieves improved stability with fewer mode collapses, and leads to generator networks with better modeling performance across a variety of architectures and objective functions.
This paper contains a collection of ideas about Generative Adversarial Networks (GAN) but it is very hard for me to get the main point of this paper. I am not saying ideas are not interesting, but I think the author needs to choose the main point of the paper, and should focus on delivering in-depth studies on the main point.
1. On the game theoretic interpretations 
The paper, Generative Adversarial Nets, NIPS 2014, already presented the game theoretic interpretations to GANs, so it's hard for me to think what's new in the section. Best response dynamics is not used in the conventional GAN training, because it's very hard to find the global optimal of inner minimization and outer maximization.
The convergence of online primal-dual gradient descent method in the minimax game is already well-known, but this analysis cannot be applied to the usual GAN setting because the objective is not convex-concave. I found this analysis would be very interesting if the authors can find the toy example when GAN becomes convex-concave by using different model parameterizations and/or different f-divergence, and conduct various studies on the convergence and stability on this problem.
I also found that the hypothesis on the model collapsing has very limited connection to the convex-concave case. It is OK to form the hypothesis and present an interesting research direction, but in order to make this as a main point of the paper, the author should provide more rigorous arguments or experimental studies instead of jumping to the hypothesis in two sentences. For example, if the authors can provide the toy example where GAN becomes convex-concave vs. non-convex-concave case, and how the loss function shape or gradient dynamics are changing, that will provide very valuable insights on the problem. 
2. DRAGAN
As open commenters pointed out, I found it's difficult to find why we want to make the norm of the gradient to 1.
Why not 2? why not 1/2? Why 1 is very special?
In the WGAN paper, the gradient is clipped to a number less than 1, because it is a sufficient condition to being 1-Lipshitz, but this paper provides no justification on this number.
It's OK not to have the theoretical answers to the questions but in that case the authors should provide ablation experiments. For example, sweeping gradient norm target from 10^-3, 10^-2, 10^-1, 1.0, 10.0, etc and their impact on the performance.
Also scheduling regularization parameter like reducing the size of lambda exponentially would be interesting as well.
Most of those studies won't be necessary if the theory is sound. However, since this paper does not provide a justification on the magic number "1", I think it's better to include some form of ablation studies.
Note that the item 1 and item 2 are not strongly related to each other, and can be two separate papers. I recommend to choose one direction and provide in-depth study on one topic. Currently, this paper tries to present interesting ideas without very deep investigations, and I cannot recommend this paper to be published.