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

Abstract

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 on the space B 1 of ideal sets. We show that if the extension is concave then the core of the game v is non-empty iff is homogeneous of degree one along the diagonal of B 1. We use this result to obtain representation theorems for the core of a non-atomic game of the form v=f 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.