Cores of Nonatomic Linear Production Games

Cores of games of the form f ∘ μ, where μ is a vector of nonatomic measures and f(z) = max{〈c, x〉 ∣ xA ≤ z, x ≥ 0} or, equivalently, f(z) = min〈z, aⁱ〉, are described in terms of μ and the data defining f. Along the way, we give a general condition on a game which implies that each measure in its core is a linear combination of a fixed finite set of nonatomic measures.