The supercore for normal-form games

We study the supercore of a system derived from a normal form game. For the case of a finite game, we define a sequence of games and show that the supercore coincides with the set of Nash equilibrium strategy profiles of the last game in that sequence. This result is illustrated with the characterization of the supercore for the n-person prisoner’s dilemma. With regard to the mixed extension of a game we prove that the supercore coincides with the set of NE whenever the game has a finite number of Nash equilibria. This coincidence is not mantained for games with infinite Nash equilibria.