Informational Smallness and Private Monitoring in Repeated Games, Second Version

46 Pages Posted: 14 Sep 2011

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: February 10, 2011

Abstract

We consider repeated games with private monitoring that are 'close' to repeated games with public/perfect monitoring. A private monitoring information structure is close to a public monitoring information structure when private signals can generate approximately the same distribution of the public signal once they are aggregated into a public signal by some public coordination device. A player.s informational size associated with the public coordination device is the key to inducing truth-telling in nearby private monitoring games when communication is possible. A player is informationally small given a public coordination device if she believes that her signal is likely to have a small impact on the public signal generated by the public coordinating device. We show that a uniformly strict equilibrium with public monitoring is robust in a certain sense: it remains an equilibrium in nearby private monitoring repeated games when the associated public coordination device, which makes private monitoring close to public monitoring, keeps every player informationally small at the same time. We also prove a new folk theorem for repeated games with private monitoring and communication by exploiting the connection between public monitoring games and private monitoring games via public coordination devices.

Keywords: Communication, Folk theorem, Informational size, Perfect monitoring, 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, Second Version (February 10, 2011). PIER Working Paper No. 11-029, Available at SSRN: https://ssrn.com/abstract=1927331 or http://dx.doi.org/10.2139/ssrn.1927331

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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