Asymptotic Measure-Based Values of Nonatomic Games

Let v = min(μ₁, μ₂, …, μ_n), where μ₁, μ₂, …, μ_n are mutually singular nonatomic probability measures, i.e., v is the market game derived from an n-glove nonatomic market with transferable utility. We describe the set of all μ-asymptotic values of v, where μ ranges over all non-atomic probability measures for which μ_i is absolutely continuous with respect to μ and dμ/dμ ∈ L₂(μ) for all 1 ≤ i ≤ n. This set is proved to be convex and relatively open.