The core of a class of non-atomic games which arise in economic applications

We study the core of a non-atomic game υ 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 ῡ on the space B₁ of ideal sets. We show that if the extension v is concave then the core of the game υ is non-empty iff ῡ is homogeneous of degree one along the diagonal of B₁. We use this result to obtain representation theorems for the core of a non-atomic game of the form υ = f o μ where μ is a finite dimensional vector of measures and f is a concave function. We also apply our results to some non-atomic games which occur in economic applications.