Values of Non-Atomic Vector Measure Games:
Are They Linear
Combinations of the Measures?
Sergiu Hart and Abraham Neyman
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.
Journal of Mathematical Economics 17 (1988), 1, 31-40