Game theory models decision makers' behaviors in strategic situations. Since the structures of games are different, behavior and preferences of the players are different in various types of game. This paper reviews various situations of games. Here, characteristics of some common games are discussed and compared. Specifically, we focus on a group of games called symmetric games including Prisoner’s Dilemma, Chicken game, Stag-Hunt and Deadlock. Scenario, outcomes, structure, and equilibrium of these games are explained and compared. Moreover, the applications of these games are discussed to show that they are not just interesting or fun problems. This review may help researchers to find appropriate symmetric games to capture the characteristics of real world strategic problems.