This study examines how two individuals make decisions in a game where they have two choices each. The researchers aimed to find specific situations where both players reach the best outcome for themselves without changing their decisions, known as Nash equilibrium. By using a method called the underline approach, they identified 81 different scenarios and categorized them into six types of equilibrium. These categories include situations where no balanced outcome exists, as well as situations where there are multiple optimal solutions. Through analyzing a real-world example involving railway and road repairs, the researchers concluded that Nash equilibrium represents a stable state in decision-making games.