This paper provides a comprehensive study of Nash Equilibrium, a fundamental concept in game theory that models strategic interactions among rational decision-makers. We begin by establishing the theoretical foundations of strategic games and the formal definition of Nash Equilibrium, then proceed to analytical techniques for identifying equilibria under both pure and mixed strategy settings. The Prisoner's Dilemma is presented as a canonical example, illustrating how rational individual decisions can lead to collectively suboptimal outcomes. The study further explores a range of methods for equilibrium identification, including dominance analysis, best-response dynamics, and computational tools such as the Lemke–Howson algorithm. Applications are examined across various fields, including economics, where firms adjust their strategies in competitive markets; political science, where electoral campaigns and international relations are modeled; behavioral sciences, where concepts such as trust and cooperation are evaluated; and artificial intelligence, where autonomous agents operate within shared environments. Additionally, this research highlights the limitations of Nash Equilibrium, particularly its assumptions of rationality, complete information, and static interactions. These challenges highlight the importance of exercising caution when applying equilibrium concepts in real-world scenarios. Through theoretical exposition, illustrative examples, and practical case studies, the paper aims to deepen understanding of how strategic decisions are formed and interpreted. By situating Nash Equilibrium in diverse contexts, this work affirms its enduring relevance while acknowledging the complexity of modeling human and institutional behavior in strategic settings.
D et al. (Thu,) studied this question.