The Game Theory and the Beautiful Mind of John Nash

In this article, we deal with Game Theory and the study of the dominant strategies equilibrium, as well as the Nash equilibrium in non-cooperative games. We make a historical narrative of the development of Game Theory and focus on John Nash's work. Introducing the main concepts involved primarily in the study of the static and non-cooperative games, we present examples of their applications. In order to show the importance of Nash's work, we discuss his biography, describing their most significant passages. Additionally, we present and discuss the motion picture about Nash's life, pointing its virtues and limitations. Finally, we highlight the main achievements of John Nash, namely his academic brilliance and his victory in the battle against a mental illness.