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The conic property for vector measure market games

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  • Omer Edhan

Abstract

We prove that every continuous value on a space of vector measure market games $$Q$$ Q , containing the space of nonatomic measures $$NA$$ N A , has the conic property, i.e., if a game $$v\in Q$$ v ∈ Q coincides with a nonatomic measure $$\nu $$ ν on a conical diagonal neighborhood then $$\varphi (v)=\nu $$ φ ( v ) = ν . We deduce that every continuous value on the linear space $$\fancyscript{M}$$ M , spanned by all vector measure market games, is determined by its values on $$\fancyscript{L}\fancyscript{M}$$ L M - the space of vector measure market games which are Lipschitz functions of the measures. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Omer Edhan, 2015. "The conic property for vector measure market games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(2), pages 377-386, May.
    • Handle: RePEc:spr:jogath:v:44:y:2015:i:2:p:377-386
    DOI: 10.1007/s00182-014-0434-x
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    References listed on IDEAS

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    1. Dubey, Pradeep & Neyman, Abraham, 1984. "Payoffs in Nonatomic Economies: An Axiomatic Approach," Econometrica, Econometric Society, vol. 52(5), pages 1129-1150, September.
    2. Abraham Neyman, 1977. "Continuous Values are Diagonal," Mathematics of Operations Research, INFORMS, vol. 2(4), pages 338-342, November.
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    1. Omer Edhan, 2016. "Values of vector measure market games and their representations," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 411-433, March.

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    Keywords

    Shapley value; Nonatomic games;

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