Analyzing the different behaviors involved in interactive decisions can help predict likely outcomes and, in turn, benefit society. Games have three main forms, which are pure coordination, strictly competitive, and mixed motivation, which push players to fully cooperate, move forward thinking only of individual needs, or compromise between the two. Profits are part of every game and the utility for each player is determined by completeness, transitivity and lottery to ensure that he is a rational decision maker. Some of the key approaches used to obtain these utilities are dominant strategy, best response, and Nash equilibrium. Nash equilibrium has become the centerpiece of game theory because it sheds light on the motivation involved in maximizing utility and how players use common knowledge and rationality to achieve this goal. These fundamental ideas and key concepts of game theory should be carefully studied and analyzed to benefit from them