Approximately Stable, School Optimal, and Student-Truthful Many-to-One Matchings (via Differential Privacy)

We present a mechanism for computing asymptotically stable school optimal matchings, while guaranteeing that it is an asymptotic dominant strategy for every student to report their true preferences to the mechanism. Our main tool in this endeavor is differential privacy: we give an algorithm that coordinates a stable matching using differentially private signals, which lead to our truthfulness guarantee. This is the first setting in which it is known how to achieve nontrivial truthfulness guarantees for students when computing school optimal matchings, assuming worst-case preferences (for schools and students) in large markets.

[1]  Eduardo M. Azevedo,et al.  STRATEGYPROOFNESS IN THE LARGE 1 1 Introduction , 2012 .

[2]  B. Pittel.  On Likely Solutions of a Stable Marriage Problem , 1992 .

[3]  Parag A. Pathak,et al.  Strategy-Proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match , 2009 .

[4]  A. Roth,et al.  The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design , 1999, The American economic review.

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

[6]  Nicole Immorlica,et al.  Marriage, honesty, and stability , 2005, SODA '05.

[7]  Kobbi Nissim,et al.  Privacy-aware mechanism design , 2011, EC '12.

[8]  Mechanism Design in Large Games: Incentives and Privacy , 2014 .

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

[10]  Elaine Shi,et al.  Private and Continual Release of Statistics , 2010, ICALP.

[11]  A. Roth.  The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory , 1984, Journal of Political Economy.

[12]  Aaron Roth,et al.  Asymptotically truthful equilibrium selection in large congestion games , 2013, EC.

[13]  A. Roth.  The college admissions problem is not equivalent to the marriage problem , 1985 .

[14]  Alvin E. Roth,et al.  Strategy-Proofness Versus Efficiency in Matching with Indifferences: Redesigning the New York City High School Match , 2009 .

[15]  SangMok Lee,et al.  Incentive Compatibility of Large Centralized Matching Markets , 2017 .

[16]  L. S. Shapley,et al.  College Admissions and the Stability of Marriage , 2013, Am. Math. Mon..

[17]  Alvin E. Roth,et al.  The Economics of Matching: Stability and Incentives , 1982, Math. Oper. Res..

[18]  Jacob D. Leshno,et al.  Unbalanced random matching markets , 2013, EC '13.

[19]  Moni Naor,et al.  Differential privacy under continual observation , 2010, STOC '10.

[20]  Guy N. Rothblum,et al.  Boosting and Differential Privacy , 2010, 2010 IEEE 51st Annual Symposium on Foundations of Computer Science.

[21]  Tim Roughgarden,et al.  Private matchings and allocations , 2013, SIAM J. Comput..

[22]  Eric Budish,et al.  Strategyproofness in the large as a desideratum for market design , 2012, EC '12.

[23]  Parag A. Pathak,et al.  Appendix to "Incentives and Stability in Large Two-Sided Matching Markets" , 2009 .

[24]  Sampath Kannan,et al.  The Exponential Mechanism for Social Welfare: Private, Truthful, and Nearly Optimal , 2012, 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science.