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The Prediction Value

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Author Info

  • Maurice Koster

    (University of Amsterdam)

  • Sascha Kurz

    (University of Bayreuth, Germany)

  • Ines Lindner

    (VU University Amsterdam)

  • Stefan Napel

    (University of Bayreuth, Germany)

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    Abstract

    We introduce the prediction value (PV) as a measure of players’ informational importance in probabilistic TU games. The latter combine a standard TU game and a probability distribution over the set of coalitions. Player i’s prediction value equals the difference between the conditional expectations of v(S) when i cooperates or not. We characterize the prediction value as a special member of the class of (extended) values which satisfy anonymity, linearity and a consistency property. Every n-player binomial semivalue coincides with the PV for a particular family of probability distributions over coalitions. The PV can thus be regarded as a power index in specific cases. Conversely, some semivalues – including the Banzhaf but not the Shapley value – can be interpreted in terms of informational importance.

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    File URL: http://papers.tinbergen.nl/13188.pdf
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    Bibliographic Info

    Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 13-188/II.

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    Date of creation: 25 Nov 2013
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    Handle: RePEc:dgr:uvatin:20130188

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    Web page: http://www.tinbergen.nl

    Related research

    Keywords: influence; voting games; cooperative games; Banzhaf value; Shapley value;

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    1. René van den Brink & Agnieszka Rusinowska & Frank Steffen, 2011. "Measuring Power and Satisfaction in Societies with Opinion Leaders: An Axiomatization," Documents de travail du Centre d'Economie de la Sorbonne 11018, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
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