Informational Smallness and Private Monitoring in Repeated Games

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.