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Privacy is an essential issue in data trading markets. This work uses amechanism design approach to study the optimal market model to economize thevalue of privacy of personal data, using differential privacy. The buyer uses afinite number of randomized algorithms to get access to the owners' data in asequential-composition manner, in which each randomized algorithm isdifferentially private. Each usage of a randomized algorithm is referred to asa period. Due to the composability of differential privacy, there areinevitable privacy losses accumulated over periods. Hence, we allow the ownersto leave the market at the end of any period by making stopping decisions. Wedefine an instrumental kernel function to capture the instrumentalness ofowners' preferences and model the formation of each owner's (both intrinsic andinstrumental) preference over periods by taking into consideration thecomposability of differential privacy and the time-varying nature of privacyconcerns. Our desideratum is to study the buyer's design regime of optimalmarket models in a dynamic environment when each owner makes coupled decisionsof stopping and reporting of their preferences. The buyer seeks to design aprivacy allocation rule that dynamically specifies the degree of privacyprotections and a payment rule to compensate for the privacy losses of theowners. The buyer additionally chooses a payment rule which is independent ofowners' reports of their preferences to influence the owners' stoppingdecisions. We characterize the dynamic incentive compatibility and provide adesign principle to construct the payment rules in terms of the privacyallocation rule. Further, we relax the buyer's market design problem andprovide a sufficient condition for an approximated dynamic incentive-compatiblemarket model.

On the Differential Private Data Market: Endogenous Evolution, Dynamic Pricing, and Incentive Compatibility