Abstract
A traditionally desired goal when designing auction mechanisms is incentive compatibility, i.e., ensuring that bidders fare best by truthfully reporting their preferences. A complementary goal, which has, thus far, received significantly less attention, is to preserve privacy, i.e., to ensure that bidders reveal no more information than necessary. We further investigate and generalize the approximate privacy model for two-party communication recently introduced by Feigenbaum et al. [8]. We explore the privacy properties of a natural class of communication protocols that we refer to as “dissection protocols”. Dissection protocols include, among others, the bisection auction in [9,10] and the bisection protocol for the millionaires problem in [8]. Informally, in a dissection protocol the communicating parties are restricted to answering simple questions of the form “Is your input between the values α and β (under a pre-defined order over the possible inputs)?”.
We prove that for a large class of functions called tiling functions, which include the 2nd-price Vickrey auction, there always exists a dissection protocol that provides a constant average-case privacy approximation ratio for uniform or “almost uniform” probability distributions over inputs. To establish this result we present an interesting connection between the approximate privacy framework and basic concepts in computational geometry. We show that such a good privacy approximation ratio for tiling functions does not, in general, exist in the worst case. We also discuss extensions of the basic setup to more than two parties and to non-tiling functions, and provide calculations of privacy approximation ratios for two functions of interest.
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References
Ghosh, A., Roughgarden, T., Sundararajan, M.: Universally utility-maximizing privacy mechanisms. In: 41st ACM Symp. on Theory of Computing, pp. 351–360 (2009)
Berman, P., DasGupta, B., Muthukrishnan, S.: On the Exact Size of the Binary Space Partitioning of Sets of Isothetic Rectangles with Applications. SIAM Journal of Discrete Mathematics 15(2), 252–267 (2002)
Bar-Yehuda, R., Chor, B., Kushilevitz, E., Orlitsky, A.: Privacy, additional information, and communication. IEEE Trans. on Inform. Theory 39, 55–65 (1993)
d’Amore, F., Franciosa, P.G.: On the optimal binary plane partition for sets of isothetic rectangles. Information Processing Letters 44, 255–259 (1992)
Chaum, D., Crépeau, C., Damgaard, I.: Multiparty, unconditionally secure protocols. In: 22th ACM Symposium on Theory of Computing, pp. 11–19 (1988)
Chor, B., Kushilevitz, E.: A zero-one law for boolean privacy. SIAM Journal of Discrete Mathematics 4, 36–47 (1991)
Dwork, C.: Differential privacy. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4052, pp. 1–12. Springer, Heidelberg (2006)
Feigenbaum, J., Jaggard, A., Schapira, M.: Approximate Privacy: Foundations and Quantification. In: ACM Conference on Electronic Commerce, pp. 167–178 (2010)
Grigorievaa, E., Heringsb, P.J.-J., Müllera, R., Vermeulena, D.: The communication complexity of private value single-item auctions. Operations Research Letters 34, 491–498 (2006)
Grigorievaa, E., Heringsb, P.J.-J., Müllera, R., Vermeulena, D.: The private value single item bisection auction. Economic Theory 30, 107–118 (2007)
Kushilevitz, E., Nisan, N.: Communication Complexity. Cambridge University Press, Cambridge (1997)
Kifer, D., Lin, B.-R.: An Axiomatic View of Statistical Privacy and Utility. Journal of Privacy and Confidentiality (to appear)
Kushilevitz, E.: Privacy and communication complexity. SIAM Journal of Discrete Mathematics 5(2), 273–284 (1992)
Paterson, M., Yao, F.F.: Efficient binary space partitions for hidden-surface removal and solid modeling. Discrete & Computational Geometry 5(1), 485–503 (1990)
Paterson, M., Yao, F.F.: Optimal binary space partitions for orthogonal objects. Journal of Algorithms 13, 99–113 (1992)
Yao, A.C.: Some complexity questions related to distributive computing. In: 11th ACM Symposium on Theory of Computing, pp. 209–213 (1979)
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Comi, M., DasGupta, B., Schapira, M., Srinivasan, V. (2011). On Communication Protocols That Compute Almost Privately. In: Persiano, G. (eds) Algorithmic Game Theory. SAGT 2011. Lecture Notes in Computer Science, vol 6982. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24829-0_6
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DOI: https://doi.org/10.1007/978-3-642-24829-0_6
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