Values of Non-Atomic Vector Measure Games:
Are They Linear Combinations of the Measures?

Sergiu Hart and Abraham Neyman


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Abstract
Consider non-atomic vector-measure games; i.e., games v of the form v = f (μ1, ..., μn), where (μ1, ..., μn) is a vector of non-atomic non-negative measures and f is a real-valued function defined on the range of (μ1, ..., μn). 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, ..., μn (this is in contrast to all the values known to date). Moreover, this happens even for market games in pNA. In the economic models, this means that the value allocations are not necessarily generated by prices. All the examples we present are special cases of a new class of values.