Informational Smallness and Private Monitoring in Repeated Games

Richard McLean (), Ichiro Obara () and Andrew Postlewaite ()
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Richard McLean: Department of Economics, Rutgers University

PIER Working Paper Archive from Penn Institute for Economic Research, Department of Economics, University of Pennsylvania

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 approxi-mately 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 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 (search for similar items in EconPapers)
JEL-codes: C72 C73 D82 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-gth
Date: 2001-05-01, Revised 2005-07-20
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Working Paper: Informational Smallness and Private Monitoring in Repeated Games (2005)
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