Informational Smallness and Private Monitoring in Repeated Games

35 Pages Posted: 8 Sep 2005

See all articles by Richard P. McLean

Richard P. McLean

Rutgers University - Department of Economics

Ichiro Obara

University of California, Los Angeles (UCLA) - Department of Economics

Andrew Postlewaite

University of Pennsylvania - Department of Economics

Date Written: July 20, 2005

Abstract

For repeated games with noisy private monitoring and communication, we examine robustness of perfect public equilibrium/subgame perfect equilibrium when private monitoring is close to some public monitoring. Private monitoring is close. to public monitoring if the private signals can generate approximately the same public signal once they are aggregated. Two key notions on private monitoring are introduced: Informational Smallness and Distributional Variability. A player is informationally small if she believes that her signal is likely to have a small impact when private signals are aggregated to generate ate a public signal. Distributional variability measures the variation in a player's conditional beliefs over the generated public signal as her private signal varies. When informational size is small relative to distributional variability (and private signals are sufficiently close to public monitoring), a uniformly strict equilibrium with public monitoring remains an equilibrium with private monitoring and communication. To demonstrate that uniform strictness is not overly restrictive, we prove a uniform folk theorem with public monitoring which, combined with our robustness result, yields a new folk theorem for repeated games with private monitoring and communication.

Keywords: Communication, Informational size, Perfect Public Equilibrium, Private monitoring, Public monitoring, Repeated games, Robustness

JEL Classification: C72, C73, D82

Suggested Citation

McLean, Richard P. and Obara, Ichiro and Postlewaite, Andrew, Informational Smallness and Private Monitoring in Repeated Games (July 20, 2005). PIER Working Paper No. 05-024, Available at SSRN: https://ssrn.com/abstract=796946 or http://dx.doi.org/10.2139/ssrn.796946

Richard P. McLean

Rutgers University - Department of Economics ( email )

75 Hamilton Street
New Jersey Hall
New Brunswick, NJ 08901
United States
732-932-7709 (Phone)
732-932-7416 (Fax)

Ichiro Obara

University of California, Los Angeles (UCLA) - Department of Economics ( email )

Box 951477
Los Angeles, CA 90095-1477
United States

Andrew Postlewaite (Contact Author)

University of Pennsylvania - Department of Economics ( email )

Ronald O. Perelman Center for Political Science
133 South 36th Street
Philadelphia, PA 19104-6297
United States
215-898-7350 (Phone)
215-573-2057 (Fax)

HOME PAGE: http://www.econ.upenn.edu/~apostlew

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