Game theory provides a formal framework for modeling strategic interactions between rational decision-makers. In the context of Artificial Intelligence (Al), game theory plays a crucial role in multi-agent systems (MAS), reinforcement learning (RL), and competitive decision-making environments. This paper explores the application of Nash Equilibria in multi-agent reinforcement learning (MARL), examining how AI agents can learn optimal strategies through interaction with other agents in both cooperative and competitive settings. We discuss the mathematical formulation of Nash Equilibria, the challenges in applying game theory to MARL, and the impact of these concepts on real-world Al applications such as autonomous systems, robotics, and adversarial gaming. Finally, we review recent advances in Al that utilize game-theoretic approaches for strategic decision-making and highlight future directions for research.