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On the Number of alpha-Pivotal Players

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Abstract

We show that bounds like those of Al-Najjar and Smorodinsky (J. Econ. Theory, 2000) as well as of Gradwohl et al. (Math. Oper. Res., 2009) on the number of alpha-pivotal agents can be obtained by decomposition of variance. All these bounds have a similar asymptotic behaviour, up to constant factors. Our bound is weaker than that of Al-Najjar and Smorodinsky, but we require only pairwise independent—rather than independent—types. Our result strengthens the bound of Gradwohl et al.

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  • Johannes Gerd Becker, 2011. "On the Number of alpha-Pivotal Players," CER-ETH Economics working paper series 11/142, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
    • Handle: RePEc:eth:wpswif:11-142
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    File URL: https://www.ethz.ch/content/dam/ethz/special-interest/mtec/cer-eth/cer-eth-dam/documents/working-papers/WP-11-142.pdf
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    References listed on IDEAS

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    1. Ronen Gradwohl & Omer Reingold & Ariel Yadin & Amir Yehudayoff, 2009. "Players' Effects Under Limited Independence," Mathematics of Operations Research, INFORMS, vol. 34(4), pages 971-980, November.
    2. George J. Mailath & Andrew Postlewaite, 1990. "Asymmetric Information Bargaining Problems with Many Agents," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(3), pages 351-367.
    3. Al-Najjar, Nabil I. & Smorodinsky, Rann, 2007. "The efficiency of competitive mechanisms under private information," Journal of Economic Theory, Elsevier, vol. 137(1), pages 383-403, November.
    4. Hans Gersbach, 2009. "Democratic Mechanisms," Journal of the European Economic Association, MIT Press, vol. 7(6), pages 1436-1469, December.
    5. Al-Najjar, Nabil I. & Smorodinsky, Rann, 2001. "Large Nonanonymous Repeated Games," Games and Economic Behavior, Elsevier, vol. 37(1), pages 26-39, October.
    6. Al-Najjar, Nabil I., 2001. "A reputational model of authority," Journal of Economic Behavior & Organization, Elsevier, vol. 46(2), pages 165-191, October.
    7. Al-Najjar, Nabil I. & Smorodinsky, Rann, 2000. "Provision of a public good with bounded cost," Economics Letters, Elsevier, vol. 67(3), pages 297-301, June.
    8. Birulin, Oleksii, 2006. "Public goods with congestion," Journal of Economic Theory, Elsevier, vol. 129(1), pages 289-299, July.
    9. Gerardi, Dino & Yariv, Leeat, 2008. "Information acquisition in committees," Games and Economic Behavior, Elsevier, vol. 62(2), pages 436-459, March.
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    1. Johannes Gerd Becker, 2012. "A Note on the Number of (alpha) -Pivotal Players," Mathematics of Operations Research, INFORMS, vol. 37(1), pages 196-200, February.

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    JEL classification:

    • D62 - Microeconomics - - Welfare Economics - - - Externalities
    • D89 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Other

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