Pivotal Players and the Characterization of Influence

Nabil I. Al-Najjar and Rann Smorodinsky

No 1174R, Discussion Papers from Northwestern University, Center for Mathematical Studies in Economics and Management Science

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.

Date: 1996-11
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.kellogg.northwestern.edu/research/math/papers/1174.pdf main text (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:nwu:cmsems:1174r

Ordering information: This working paper can be ordered from

Access Statistics for this paper

More papers in Discussion Papers from Northwestern University, Center for Mathematical Studies in Economics and Management Science Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014. Contact information at EDIRC.
Bibliographic data for series maintained by Fran Walker ( this e-mail address is bad, please contact ).