Continuous Values of Market Games are Conic

Authors: 
Omer Edhan
Abstract: 

We prove that every continuous value on a space of vector measure market games $Q$, containing the space of nonatomic measures $NA$, has the \textit{conic property}, i.e., if a game $v\in Q$ coincides with a nonatomic measure $\nu$ on a conical diagonal neighborhood then $\varphi(v)=\nu$. 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 $\mathcal{LM}$ - the space of vector measure market games which are Lipschitz functions of the measures.

Date: 
August, 2012
Number: 
623