Selling privacy at auction

We initiate the study of markets for private data, through the lens of differential privacy. Although the purchase and sale of private data has already begun on a large scale, a theory of privacy as a commodity is missing. In this paper, we propose to build such a theory. Specifically, we consider a setting in which a data analyst wishes to buy information from a population from which he can estimate some statistic. The analyst wishes to obtain an accurate estimate cheaply, while the owners of the private data experience some cost for their loss of privacy, and must be compensated for this loss. Agents are selfish, and wish to maximize their profit, so our goal is to design truthful mechanisms. Our main result is that such problems can naturally be viewed and optimally solved as variants of multi-unit procurement auctions. Based on this result, we derive auctions which are optimal up to small constant factors for two natural settings: When the data analyst has a fixed accuracy goal, we show that an application of the classic Vickrey auction achieves the analyst's accuracy goal while minimizing his total payment. When the data analyst has a fixed budget, we give a mechanism which maximizes the accuracy of the resulting estimate while guaranteeing that the resulting sum payments do not exceed the analyst's budget.