Private Private Information

TL;DR

This paper introduces the concept of private private signals, which contain information about an unknown state but not about other signals, exploring their informativeness and optimality under privacy constraints.

Contribution

It formalizes private private signals, characterizes their optimal informativeness, and discusses implications for various fields like recommendation systems and mechanism design.

Findings

Private private signals can be optimal under certain privacy constraints.

Trade-offs exist between signal quality and privacy preservation.

The paper provides a framework for designing privacy-preserving information structures.

Abstract

Private signals model noisy information about an unknown state. Although these signals are called "private," they may still carry information about each other. Our paper introduces the concept of private private signals, which contain information about the state but not about other signals. To achieve privacy, signal quality may need to be sacrificed. We study the informativeness of private private signals and characterize those that are optimal in the sense that they cannot be made more informative without violating privacy. We discuss implications for privacy in recommendation systems, information design, causal inference, and mechanism design.