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

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 ${\overline {v}}$ on the space B1 of ideal sets. We show that if the extension ${\overline {v}}$ is concave then the core of the game v is non-empty iff ${\overline {v}}$ 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 v=fˆ 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.