Informational Smallness and Private Monitoring in Repeated Games

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 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 su¢ ciently 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.