Values of non-atomic vector measure games. Are they linear combinations of the measures?

Consider non-atomic vector measure games; i.e., games v of the form v = f{hook} {ring operator}(μ₁,...,μ_n, where (μ₁,...,μ_n) is a vector of non-atomic non-negative measures and f{hook} is a real-valued function defined on the range of (μ₁,...,μ_n). Games of this form arise, for example, from production models and from finite-type markets. We show that the value of such a game need not be a linear combination of the measures μ₁,...,μ_n (this is in contrast to all the values known to date). Moreover, this happens even for market games in pN A. In the economic models, thismeans that the value allocations are not necessarily generated by prices. All the examples we present are special cases of a new class of values.