The weak-core of a game in normal form with a continuum of players

This paper deals with the weak-core of normal form games with a continuum set of players and without side payments. This concept is an approximation of the core introduced by Weber, Shapley and Shubik. The weak-core is slightly larger than Aumann's α-core when adapted to large anonymous games. A non-emptiness result is obtained based on the well known Scarf's non-vacuity theorem for finite games.