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Personal information and other types of private data are valuable for both data owners and institutions interested in providing targeted and customized services that require analyzing such data. In this context, privacy is sometimes seen as a commodity: institutions (data buyers) pay individuals (or data sellers) in exchange for private data. In this study, we examine the problem of designing such data contracts, through which a buyer aims to minimize his payment to the sellers for a desired level of data quality, while the latter aim to obtain adequate compensation for giving up a certain amount of privacy. Specifically, we use the concept of differential privacy and examine a model of linear and nonlinear queries on private data. We show that conventional algorithms that introduce differential privacy via zero-mean noise fall short for the purpose of such transactions as they do not provide sufficient degree of freedom for the contract designer to negotiate between the competing interests of the buyer and the sellers. Instead, we propose a biased differentially private algorithm which allows us to customize the privacy-accuracy tradeoff for each individual. We use a contract design approach to find the optimal contracts when using this biased algorithm to provide privacy, and show that under this combination the buyer can achieve the same level of accuracy with a lower payment as compared to using the unbiased algorithms, while incurring lower privacy loss for the sellers.

Contract design for purchasing private data using a biased differentially private algorithm