The supercore of a normal form game system is studied. For finite games with pure strategies, the supercore matches the Nash equilibrium strategy profiles of the last game in a sequence. This is shown with the n-person prisoners' dilemma. In games with a finite number of Nash equilibria, the set of Nash equilibrium profiles is the same as the supercore. However, for games with an infinite number of Nash equilibria, this may not hold true unless a specific binary relation is present.