Existence of efficient envy-free allocations of a heterogeneous divisible commodity with nonadditive utilities
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 on the space B1 of ideal sets. We show that if the extension v is concave then the core of the game v is non-empty i ̈ v is homogeneous of degree one along the diagonal of B1. We use this result to obtain representation theorems for the core of a nonatomic game of the form v f m where m is a ®nite dimensional vector of measures and f is a concave function. We also apply our results to some nonatomic games which occur in economic applications.