  Privacy is an essential issue in data trading markets. This work uses a
mechanism design approach to study the optimal market model to economize the
value of privacy of personal data, using differential privacy. The buyer uses a
finite number of randomized algorithms to get access to the owners' data in a
sequential-composition manner, in which each randomized algorithm is
differentially private. Each usage of a randomized algorithm is referred to as
a period. Due to the composability of differential privacy, there are
inevitable privacy losses accumulated over periods. Hence, we allow the owners
to leave the market at the end of any period by making stopping decisions. We
define an instrumental kernel function to capture the instrumentalness of
owners' preferences and model the formation of each owner's (both intrinsic and
instrumental) preference over periods by taking into consideration the
composability of differential privacy and the time-varying nature of privacy
concerns. Our desideratum is to study the buyer's design regime of optimal
market models in a dynamic environment when each owner makes coupled decisions
of stopping and reporting of their preferences. The buyer seeks to design a
privacy allocation rule that dynamically specifies the degree of privacy
protections and a payment rule to compensate for the privacy losses of the
owners. The buyer additionally chooses a payment rule which is independent of
owners' reports of their preferences to influence the owners' stopping
decisions. We characterize the dynamic incentive compatibility and provide a
design principle to construct the payment rules in terms of the privacy
allocation rule. Further, we relax the buyer's market design problem and
provide a sufficient condition for an approximated dynamic incentive-compatible
market model.
