Values of nondifferentiable vector measure games

Omer Edhan

doi:10.1007/s00182-012-0348-4

Values of nondifferentiable vector measure games

Omer Edhan

Economics

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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. © 2012 Springer-Verlag Berlin Heidelberg.

Original language	English
Pages (from-to)	947-972
Number of pages	25
Journal	International Journal of Game Theory
Volume	42
Issue number	4
DOIs	https://doi.org/10.1007/s00182-012-0348-4
Publication status	Published - Nov 2013

Keywords

Nonatomic games
Shapley value

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10.1007/s00182-012-0348-4

POST-PEER-REVIEW-NON-PUBLISHERS.PDFAccepted author manuscript, 389 KB

http://www.springerlink.com/content/lq78n2m3l0664228/

Cite this

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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. {\textcopyright} 2012 Springer-Verlag Berlin Heidelberg.",

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AB - 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. © 2012 Springer-Verlag Berlin Heidelberg.

KW - Nonatomic games

KW - Shapley value

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DO - 10.1007/s00182-012-0348-4

M3 - Article

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VL - 42

SP - 947

EP - 972

JO - International Journal of Game Theory

JF - International Journal of Game Theory

IS - 4

ER -

Values of nondifferentiable vector measure games

Abstract

Keywords

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