Generative Adversarial Networks (GANs) represent a revolutionary framework in unsupervised learning, where a generator and a discriminator interact adversarially to produce and classify synthetic data. This paper restructures the GAN training dynamics through a game-theoretic lens, introducing Nash bargaining and the take-it-or-leave-it (TIOLI) mechanism to model generatordiscriminator interactions. By framing the interaction as a cooperative bargaining problem, the proposed framework emphasizes balancing utility for the discriminator and cost minimization for the generator. Theoretical results demonstrate that the framework achieves stable and efficient GAN training, aligning the objectives of both entities. This work contributes to a deeper theoretical understanding of GANs and reinforces the theoretical foundation of GANs.