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Continuous Values of Market Games are Conic

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  • 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.

Suggested Citation

  • Omer Edhan, 2012. "Continuous Values of Market Games are Conic," Discussion Paper Series dp623, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp623
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    References listed on IDEAS

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    1. Abraham Neyman, 1977. "Continuous Values are Diagonal," Mathematics of Operations Research, INFORMS, vol. 2(4), pages 338-342, November.
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    Cited by:

    1. Edhan, Omer, 2015. "Payoffs in exact TU economies," Journal of Economic Theory, Elsevier, vol. 155(C), pages 152-184.
    2. Omer Edhan, 2012. "Values of Exact Market Games," Discussion Paper Series dp627, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    3. Omer Edhan, 2012. "Payoffs in Nondifferentiable Perfectly Competitive TU Economies," Discussion Paper Series dp629, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.

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