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A Characterization of Exact Non-atomic Market Games

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  • Massimiliano AMARANTE

Abstract

Continuous exact non-atomic games are naturally associated to certain operators between Banach spaces. It thus makes sense to study games by means of the corresponding operators. We characterize non-atomic exact market games in terms of the properties of the associated operators. We also prove a separation theorem for weak compact sets of countably additive measures, which is of independent interest.

Suggested Citation

  • Massimiliano AMARANTE, 2013. "A Characterization of Exact Non-atomic Market Games," Cahiers de recherche 12-2013, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    • Handle: RePEc:mtl:montec:12-2013
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    References listed on IDEAS

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    1. Massimiliano Amarante & Luigi Montrucchio, 2010. "The bargaining set of a large game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(3), pages 313-349, June.
    2. Massimiliano Amarante & Fabio Maccheroni, 2006. "When an Event Makes a Difference," Theory and Decision, Springer, vol. 60(2), pages 119-126, May.
    3. Hart, Sergiu, 1977. "Values of non-differentiable markets with a continuum of traders," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 103-116, August.
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    5. MERTENS, Jean-François, 1980. "Values and derivatives," LIDAM Reprints CORE 435, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. M. Amarante & F. Maccheroni & M. Marinacci & L. Montrucchio, 2006. "Cores of non-atomic market games," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(3), pages 399-424, October.
    7. Itzhak Gilboa, 2004. "Uncertainty in Economic Theory," Post-Print hal-00756317, HAL.
    8. Jean-François Mertens, 1980. "Values and Derivatives," Mathematics of Operations Research, INFORMS, vol. 5(4), pages 523-552, November.
    9. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, July.
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    Citations

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    Cited by:

    1. Denis Belomestny & Volker Kraetschmer, 2017. "Minimax theorems for American options in incomplete markets without time-consistency," Papers 1708.08904, arXiv.org.
    2. Denis Belomestny & Tobias Hübner & Volker Krätschmer & Sascha Nolte, 2019. "Minimax theorems for American options without time-consistency," Finance and Stochastics, Springer, vol. 23(1), pages 209-238, January.
    3. Corina Birghila & Tim J. Boonen & Mario Ghossoub, 2023. "Optimal insurance under maxmin expected utility," Finance and Stochastics, Springer, vol. 27(2), pages 467-501, April.

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    More about this item

    Keywords

    lower/upper envelopes; separation theorem; exact games; nonatomic market games;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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