The core in cooperative game theory is determined by specific properties like individual rationality, superadditivity, and reduced game property. These properties play a crucial role in defining stable solutions in different types of games. For example, the prenucleolus is characterized by the reduced game property, the Shapley value by superadditivity, and the prekernel by reduced game property and other assumptions. The core of transferable utility games and non-transferable utility games have distinct characteristics based on these properties. The chapter discusses various properties of solutions in coalitional games, the core of balanced games, market games, and games with coalition structures.