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A characterization of exact non-atomic market games

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  • Amarante, Massimiliano

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 non-atomic measures, which is of independent interest.

Suggested Citation

  • Amarante, Massimiliano, 2014. "A characterization of exact non-atomic market games," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 59-62.
    • Handle: RePEc:eee:mateco:v:54:y:2014:i:c:p:59-62
    DOI: 10.1016/j.jmateco.2014.08.005
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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.
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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.
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    Cited by:

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    More about this item

    Keywords

    Non-additive set functions; Integral vector measure; Lower/upper envelopes; Separation theorem; Exact games; Non-atomic market games;
    All these keywords.

    JEL classification:

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

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