The conic property for vector measure market games

We prove that every continuous value on a space of vector measure market games $Q$ , containing the space of nonatomic measures $NA$ , has the conic property, i.e., if a game $v\in Q$ coincides with a nonatomic measure $\mathit{\nu }$ on a conical diagonal neighborhood then $\mathit{\phi }(v)=\mathit{\nu }$ . We deduce that every continuous value on the linear space $\mathcal{M}$ , spanned by all vector measure market games, is determined by its values on $\mathcal{L}\mathcal{M}$ ‐ the space of vector measure market games which are Lipschitz functions of the measures.