Working Paper: CEPR ID: DP13536
Authors: Kfir Eliaz; Ran Eilat; Xiaosheng Mu
Abstract: Modern information technologies make it possible to store, analyze and trade unprecedented amounts of detailed information about individuals. This has led to public discussions on whether individuals' privacy should be better protected by restricting the amount or the precision of information that is collected by commercial institutions on its participants. We contribute to this discussion by proposing a Bayesian approach to measure loss of privacy and applying it to the design of optimal mechanisms. Specifically, we define the loss of privacy associated with a mechanism as the difference between the designer's prior and posterior beliefs about an agent's type, where this difference is calculated using Kullback-Leibler divergence, and where the change in beliefs is triggered by actions taken by the agent in the mechanism. We consider both ex-ante (the expected difference in beliefs over all type realizations cannot exceed some threshold κ) and ex-post (for every realized type, the maximal difference in beliefs cannot exceed some threshold κ) measures of privacy loss. Using these notions we study the properties of optimal privacy-constrained mechanisms and the relation between welfare/profits and privacy levels.
Keywords: privacy; mechanism design
JEL Codes: No JEL codes provided
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| optimal privacy-constrained mechanism (D82) | partitions the set of types into finitely many intervals (C46) |
| increase in privacy parameter (θ) (D89) | increase in the number of intervals (C43) |
| optimal mechanism (D47) | allows for differential privacy across consumer types (D19) |
| expected relative entropy (privacy loss) (D80) | crucial factor in the mechanism's design (D47) |
| optimal mechanism (D47) | maximizes expected profit while satisfying privacy and incentive compatibility constraints (D82) |