The Exponential Mechanism for Social Welfare: Private, Truthful, and Nearly Optimal

In this paper we show that for any mechanism design problem with the objective of maximizing social welfare, the exponential mechanism can be implemented as a truthful mechanism while still preserving differential privacy. Our instantiation of the exponential mechanism can be interpreted as a generalization of the VCG mechanism in the sense that the VCG mechanism is the extreme case when the privacy parameter goes to infinity. To our knowledge, this is the first general tool for designing mechanisms that are both truthful and differentially private.

[1]  J. Rochet.  A necessary and sufficient condition for rationalizability in a quasi-linear context , 1987 .

[2]  Mark Jerrum,et al.  Approximating the Permanent , 1989, SIAM J. Comput..

[3]  Vidyadhar G. Kulkarni,et al.  Generating Random Combinatorial Objects , 1990, J. Algorithms.

[4]  Eric Vigoda,et al.  A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries , 2004, JACM.

[5]  Cynthia Dwork,et al.  Calibrating Noise to Sensitivity in Private Data Analysis , 2006, TCC.

[6]  Daniel A. Spielman,et al.  Spectral Graph Theory and its Applications , 2007, 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07).

[7]  Kunal Talwar,et al.  Mechanism Design via Differential Privacy , 2007, 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07).

[8]  A. Blum,et al.  A learning theory approach to non-interactive database privacy , 2008, STOC.

[9]  Cynthia Dwork,et al.  Differential Privacy: A Survey of Results , 2008, TAMC.

[10]  Christos H. Papadimitriou,et al.  On the Hardness of Being Truthful , 2008, 2008 49th Annual IEEE Symposium on Foundations of Computer Science.

[11]  Anna R. Karlin,et al.  Auctions for structured procurement , 2008, SODA '08.

[12]  A. Ny,et al.  Introduction to (generalized) Gibbs measures , 2007, Ensaios Matemáticos.

[13]  Shuchi Chawla,et al.  Sequential Posted Pricing and Multi-parameter Mechanism Design , 2010, ArXiv.

[14]  Shahar Dobzinski,et al.  On the Power of Randomization in Algorithmic Mechanism Design , 2009, 2009 50th Annual IEEE Symposium on Foundations of Computer Science.

[15]  Moshe Babaioff,et al.  Truthful mechanisms with implicit payment computation , 2010, EC '10.

[16]  Tim Roughgarden,et al.  Black-Box Randomized Reductions in Algorithmic Mechanism Design , 2010, 2010 IEEE 51st Annual Symposium on Foundations of Computer Science.

[17]  Aaron Roth,et al.  Differentially private combinatorial optimization , 2009, SODA '10.

[18]  Tim Roughgarden,et al.  Algorithmic Game Theory , 2007 .

[19]  Gagan Goel,et al.  Budget constrained auctions with heterogeneous items , 2009, STOC '10.

[20]  Amin Saberi,et al.  An O(log n/ log log n)-approximation algorithm for the asymmetric traveling salesman problem , 2010, SODA '10.

[21]  Amin Saberi,et al.  An O(log n/ log log n)-approximation algorithm for the asymmetric traveling salesman problem , 2010, SODA '10.

[22]  Shuchi Chawla,et al.  Multi-parameter mechanism design and sequential posted pricing , 2010, BQGT.

[23]  C. Dwork.  A firm foundation for private data analysis , 2011, Commun. ACM.

[24]  Shaddin Dughmi,et al.  A truthful randomized mechanism for combinatorial public projects via convex optimization , 2011, EC '11.

[25]  Robert D. Kleinberg,et al.  Bayesian incentive compatibility via matchings , 2011, SODA '11.

[26]  Tim Roughgarden,et al.  From convex optimization to randomized mechanisms: toward optimal combinatorial auctions , 2011, STOC.

[27]  Aaron Roth,et al.  Selling privacy at auction , 2010, EC '11.

[28]  Xiaohui Bei,et al.  Bayesian incentive compatibility via fractional assignments , 2010, SODA '11.

[29]  Jan Vondrák,et al.  Limitations of Randomized Mechanisms for Combinatorial Auctions , 2011, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science.

[30]  Moshe Tennenholtz,et al.  Approximately optimal mechanism design via differential privacy , 2010, ITCS '12.

[31]  Ian A. Kash,et al.  Truthful mechanisms for agents that value privacy , 2011, EC.

[32]  David Xiao,et al.  Is privacy compatible with truthfulness? , 2013, ITCS '13.