The past decade has witnessed a drastic increase in modern deep neural networks (DNNs) size, especially for generative adversarial networks (GANs). Since GANs usually suffer from high computational complexity, researchers have shown an increased interest in applying pruning methods to reduce the training and inference costs of GANs. Among different pruning methods invented for supervised learning, dynamic sparse training (DST) has gained increasing attention recently as it enjoys excellent training efficiency with comparable performance to post-hoc pruning. Hence, applying DST on GANs, where we train a sparse GAN with a fixed parameter count throughout training, seems to be a good candidate for reducing GAN training costs. However, a few challenges, including the degrading training instability, emerge due to the adversarial nature of GANs. Hence, we introduce a quantity called balance ratio (BR) to quantify the balance of the generator and the discriminator. We conduct a series of experiments to show the importance of BR in understanding sparse GAN training. Building upon single dynamic sparse training (SDST), where only the generator is adjusted during training, we propose double dynamic sparse training (DDST) to control the BR during GAN training. Empirically, DDST automatically determines the density of the discriminator and greatly boosts the performance of sparse GANs on multiple datasets.