Advertisement

On the Impossibility of Black-Box Transformations in Mechanism Design

  • Rafael Pass
  • Karn Seth
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8768)

Abstract

A fundamental question in algorithmic mechanism design is whether any approximation algorithm for a single-parameter social-welfare maximization problem can be turned into a dominant-strategy truthful mechanism for the same problem (while preserving the approximation ratio up to a constant factor). A particularly desirable type of transformations—called black-box transformations—achieve the above goal by only accessing the approximation algorithm as a black box.

A recent work by Chawla, Immorlica and Lucier (STOC 2012) demonstrates (unconditionally) the impossibility of certain restricted classes of black-box transformations—where the tranformation is oblivious to the feasibility constrain of the optimization problem. In this work, we remove these restrictions under standard complexity-theoretic assumptions: Assuming the existence of one-way functions, we show the impossibility of all black-box transformations.

Keywords

Approximation Algorithm Problem Instance Approximation Ratio Commitment Scheme Impossibility Result 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [BGI+12]
    Barak, B., Goldreich, O., Impagliazzo, R., Rudich, S., Sahai, A., Vadhan, S.P., Yang, K.: On the (im)possibility of obfuscating programs. J. ACM 59(2), 6 (2012)CrossRefMathSciNetGoogle Scholar
  2. [BH11]
    Bei, X., Huang, Z.: Bayesian incentive compatibility via fractional assignments. In: Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 720–733. SIAM (2011)Google Scholar
  3. [BR13]
    Brakerski, Z., Rothblum, G.N.: Obfuscating conjunctions. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 416–434. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  4. [CIL12]
    Chawla, S., Immorlica, N., Lucier, B.: On the limits of black-box reductions in mechanism design. In: Proceedings of the 44th Symposium on Theory of Computing, pp. 435–448. ACM (2012)Google Scholar
  5. [CRV10]
    Canetti, R., Rothblum, G.N., Varia, M.: Obfuscation of hyperplane membership. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 72–89. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  6. [GGH+13]
    Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. In: FOCS (2013)Google Scholar
  7. [Gol01]
    Goldreich, O.: Foundations of Cryptography — Basic Tools. Cambridge University Press (2001)Google Scholar
  8. [HILL99]
    Håstad, J., Impagliazzo, R., Levin, L., Luby, M.: A pseudorandom generator from any one-way function. SIAM Journal on Computing 28, 12–24 (1999)CrossRefGoogle Scholar
  9. [HKM11]
    Hartline, J.D., Kleinberg, R., Malekian, A.: Bayesian incentive compatibility via matchings. In: Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 734–747. SIAM (2011)Google Scholar
  10. [HL09]
    Hartline, J.D., Lucier, B.: Bayesian algorithmic mechanism design. CoRR, abs/0909.4756 (2009)Google Scholar
  11. [HRV+07]
    Hohenberger, S., Rothblum, G.N., Shelat, A., Vaikuntanathan, V.: Securely obfuscating re-encryption. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 233–252. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  12. [IR88]
    Impagliazzo, R., Rudich, S.: Limits on the provable consequences of one-way permutations. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 8–26. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  13. [Nao91]
    Naor, M.: Bit commitment using pseudorandomness. Journal of Cryptology 4(2), 151–158 (1991)CrossRefzbMATHGoogle Scholar
  14. [NR00]
    Nisan, N., Ronen, A.: Computationally feasible vcg mechanisms. In: ACM Conference on Electronic Commerce, pp. 242–252 (2000)Google Scholar
  15. [Wee05]
    Wee, H.: On obfuscating point functions. In: Proceedings of the Thirty-Seventh Annual ACM Symposium on Theory of Computing, pp. 523–532. ACM (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Rafael Pass
    • 1
  • Karn Seth
    • 1
  1. 1.Cornell UniversityUSA

Personalised recommendations