Generative Adversarial Network, as a promising research direction in the AI community, recently attracts considerable attention due to its ability to generating high-quality realistic data. GANs are a competing game between two neural networks trained in an adversarial manner to reach a Nash equilibrium. Despite the improvement accomplished in GANs in the last years, there remain several issues to solve. In this way, how to tackle these issues and make advances leads to rising research interests. This paper reviews literature that leverages the game theory in GANs and addresses how game models can relieve specific generative models' challenges and improve the GAN's performance. In particular, we firstly review some preliminaries, including the basic GAN model and some game theory backgrounds. After that, we present our taxonomy to summarize the state-of-the-art solutions into three significant categories: modified game model, modified architecture, and modified learning method. The classification is based on the modifications made in the basic model by the proposed approaches from the game-theoretic perspective. We further classify each category into several subcategories. Following the proposed taxonomy, we explore the main objective of each class and review the recent work in each group. Finally, we discuss the remaining challenges in this field and present the potential future research topics.