This paper will define the concept of game theory and its basic idea, as well as its development through history. Also, the classification of games and some games will be described. The most famous game, and most described, is the prisoner's dilemma. Through the game you will be introduced to the equilibrium concepts. The key term is Nash's equilibrium, which represents the balance of the best choice for both players. It was designed by Nobel Prize winner John Nash and described in the movie Beautiful Mind, filmed by the famous Nobel Prize winner. The main part will be the application of game theory in practice. Specifically, in business and making important business decisions to achieve competitive advantages. It is also shown in the example of monopoly, duopoly and oligopoly. As an example of game theory in practice was taken the rivalry between Apple and Samsung, two major and significant companies competing in the electronics market. Also, given is insight into their business and the use of prisoner's dilemma in deciding. The decisions are related to the initiation or dismissal of each other. Also, there is an example from the literacy issue on the market with a medium or large screen smartphone. Before the conclusion, there are some advantages and shortcomings of the game theory, for which is not well represented in practice.