Buying data from privacy-aware individuals: The effect of negative payments

Weina Wang, Lei Ying, Junshan Zhang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Scopus citations


We study a market model where a data analyst uses monetary incentives to procure private data from strategic data subjects/ individuals. To characterize individuals’ privacy concerns, we consider a local model of differential privacy, where the individuals do not trust the analyst so privacy costs are incurred when the data is reported to the data analyst. We investigate a basic model where the private data are bits that represent the individuals’ knowledge about an underlying state, and the analyst pays each individual according to all the reported data. The data analyst’s goal is to design a payment mechanism such that at an equilibrium, she can learn the state with an accuracy goal met and the corresponding total expected payment minimized. What makes the mechanism design more challenging is that not only the data but also the privacy costs are unknown to the data analyst, where the costs reflect individuals’ valuations of privacy and are modeled by “cost coefficients.” To cope with the uncertainty in the cost coefficients and drive down the data analyst’s cost, we utilize possible negative payments (which penalize individuals with “unacceptably” high valuations of privacy) and explore interim individual rationality. We design a family of payment mechanisms, each of which has a Bayesian Nash equilibrium where the individuals exhibit a threshold behavior: the individuals with cost coefficients above a threshold choose not to participate, and the individuals with cost coefficients below the threshold participate and report data with quality guarantee. By choosing appropriate parameters, we obtain a sequence of mechanisms, as the number of individuals grows large. Each mechanism in this sequence fulfills the accuracy goal at a Bayesian Nash equilibrium. The total expected payment at the equilibrium goes to zero; i.e., this sequence of mechanisms is asymptotically optimal.

Original languageEnglish (US)
Title of host publicationWeb and Internet Economics - 12th International Conference, WINE 2016, Proceedings
EditorsAdrian Vetta, Yang Cai
PublisherSpringer Verlag
Number of pages15
ISBN (Print)9783662541098
StatePublished - 2016
Event12th International Conference on Web and Internet Economics, WINE 2016 - Montreal, Canada
Duration: Jun 11 2016Jul 14 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10123 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other12th International Conference on Web and Internet Economics, WINE 2016

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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