We study the core of a non-atomic game v which is uniformly continuous with
respect to the DNA-topology and continuous at the grand coalition. Such a
game has a unique DNA-continuous extension (v) over bar on the space B-1 of
ideal sets. We show that if the extension (v) over bar is concave then the
core of the game v is non-empty iff (v) over bar is homogeneous of degree
one along the diagonal of B-1. We use this result to obtain representation
theorems for the core of a nonatomic game of the form v = f o mu where mu i
s a finite dimensional vector of measures and f is a concave function. We a
lso apply our results to some nonatomic games which occur in economic appli
cations.