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Pivotal Players and the Characterization of Influence

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  • Nabil I. Al-Najjar
  • Rann Smorodinsky

Abstract

A player inuences a collective outcome if his actions can change the probability of that outcome. He is Æ-pivotal if this change exceeds some threshold Æ. We study inuence in general environments with N players and arbitrary sets of signals. It is shown that inuence is maximized when players' signals are identically distributed and the outcome is determined according to simple majority rule.This leads to the surprising conclusion that majority rules already contain the maximal number of pivotal players. From this we derive a tight bound on average inuence, as well as a tight bound on the number of Æ-pivotal players, which is independent of N. This analysis is relevant to problems where players' inuence is a key consideration in determining their strategic behavior. The applications we consider include the problem of designing a mechanism for the provision of public goods in the spirit of Mailath and Postlewaite (1990), partnership games, games with production complementarities, and cooperation in a noisy prisoner's dilemma.

Suggested Citation

  • Nabil I. Al-Najjar & Rann Smorodinsky, 1996. "Pivotal Players and the Characterization of Influence," Discussion Papers 1174R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • Handle: RePEc:nwu:cmsems:1174r
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    Cited by:

    1. Al-Najjar, Nabil I., 2004. "Aggregation and the law of large numbers in large economies," Games and Economic Behavior, Elsevier, vol. 47(1), pages 1-35, April.
    2. Nabil I. Al-Najjar, 1998. "A Reputational Model of Authority," Discussion Papers 1223, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. 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.

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