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Values of nondifferentiable vector measure games

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  • Omer Edhan

Abstract

We introduce ideas and methods from distribution theory into value theory. This new approach enables us to construct new diagonal formulas for the Mertens value (Int J Game Theory 17:1–65, 1988 ) and the Neyman value (Isr J Math 124:1–27, 2001 ) on a large space of non-differentiable games. This in turn enables us to give an affirmative answer to the question, first posed by Neyman (Isr J Math 124:1–27, 2001 ), whether the Mertens value and the Neyman value coincide “modulo Banach limits”? The solution is an intermediate result towards a characterization of values of norm 1 of vector measure games with bounded variation. Copyright Springer-Verlag Berlin Heidelberg 2013

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  • Omer Edhan, 2013. "Values of nondifferentiable vector measure games," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(4), pages 947-972, November.
    • Handle: RePEc:spr:jogath:v:42:y:2013:i:4:p:947-972
    DOI: 10.1007/s00182-012-0348-4
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    1. Abraham Neyman & Rann Smorodinsky, 2004. "Asymptotic Values of Vector Measure Games," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 739-775, November.
    2. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    3. Mertens, J F, 1988. "The Shapley Value in the Non Differentiable Case," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(1), pages 1-65.
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    Keywords

    Nonatomic games; Shapley value;

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