Approximately Optimal Mechanism Design Via Differential Privacy

18 Pages Posted: 6 Mar 2012

See all articles by Kobbi Nissim

Kobbi Nissim

Georgetown University - Department of Computer Science

Rann Smorodinsky

Technion-Israel Institute of Technology - The William Davidson Faculty of Industrial Engineering & Management

Moshe Tennenholtz

Technion-Israel Institute of Technology - The William Davidson Faculty of Industrial Engineering & Management

Date Written: October 18, 2011

Abstract

We study the implementation challenge in an abstract interdependent values model and an arbitrary objective function. We design a mechanism that allows for approximate optimal implementation of insensitive objective functions in ex-post Nash equilibrium. If, furthermore, values are private then the same mechanism is strategy proof. We cast our results onto two specific models: pricing and facility location. The mechanism we design is optimal up to an additive factor of the order of magnitude of one over the square root of the number of agents and involves no utility transfers. Underlying our mechanism is a lottery between two auxiliary mechanisms — with high probability we actuate a mechanism that reduces players influence on the choice of the social alternative, while choosing the optimal outcome with high probability. This is where differential privacy is employed. With the complementary probability we actuate a mechanism that may be typically far from optimal but is incentive compatible. The joint mechanism inherits the desired properties from both.

Suggested Citation

Nissim, Kobbi and Smorodinsky, Rann and Tennenholtz, Moshe, Approximately Optimal Mechanism Design Via Differential Privacy (October 18, 2011). Available at SSRN: https://ssrn.com/abstract=2017224 or http://dx.doi.org/10.2139/ssrn.2017224

Kobbi Nissim

Georgetown University - Department of Computer Science ( email )

37th & O St., NW
St. Mary's Hall 329A
Washington, DC 20057
United States

Rann Smorodinsky (Contact Author)

Technion-Israel Institute of Technology - The William Davidson Faculty of Industrial Engineering & Management ( email )

Haifa 32000
Israel

Moshe Tennenholtz

Technion-Israel Institute of Technology - The William Davidson Faculty of Industrial Engineering & Management ( email )

Bloomfield-312
Haifa 32000
Israel
972-4-829 4419 (Phone)

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