A Bayesian Approach to Privacy in Economics

What is the effect of privacy concerns on economic activity? What are the social costs and benefits involved in imposing privacy regulations on businesses? How can economic institu- tions be designed so that their participants suffer the minimal necessary privacy loss, while still allowing the designer to achieve some desired outcome? These and similar questions are at the heart of current debates regarding privacy concerns. Yet, there is no agreed upon theoretical framework for measuring privacy (or the loss thereof) that can be integrated into mainstream economic models to address these questions. Our goal in this project is to develop such a frame-work.

The cornerstone of our approach is the idea that privacy loss is a relative notion: How much information is effectively extracted from an individual through her actions should be measured relative to what is already known about her. We introduce a notion of an “observer" who ob- serves some (or all) information about interaction of the agents in the model, and measure the agent's privacy loss by the difference between the observer's prior and posterior beliefs.

We will demonstrate the usefulness of our approach by applying it to two types of environ- ments. In the first, the observer is a third party who sees the outcome of a trading mechanism. In the second, the observer is the designer of a mechanism who sees all the participants’ actions. In these two representative environments, we will show how the interaction between privacy concerns and strategic considerations affect economic outcomes.