The success of GANs is usually attributed to properties of the divergence obtained by an optimal discriminator. In this work we show that this approach has a fundamental flaw:\ If we do not impose regularity of the discriminator, it can exploit visually imperceptible errors of the generator to always achieve the maximal generator loss. In practice, gradient penalties are used to regularize the discriminator. However, this needs a metric on the space of images that captures visual similarity. Such a metric is not known, which explains the limited success of gradient penalties in stabilizing GANs.\ Instead, we argue that the implicit competitive regularization (ICR) arising from the simultaneous optimization of generator and discriminator enables GANs performance. We show that opponent-aware modelling of generator and discriminator, as present in competitive gradient descent (CGD), can significantly strengthen ICR and thus stabilize GAN training without explicit regularization. In our experiments, we use an existing implementation of WGAN-GP and show that by training it with CGD without any explicit regularization, we can improve the inception score (IS) on CIFAR10, without any hyperparameter tuning.