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Inapproximability Results for Combinatorial Auctions with Submodular Utility Functions

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Internet and Network Economics (WINE 2005)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 3828))

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Abstract

We consider the following allocation problem arising in the setting of combinatorial auctions: a set of goods is to be allocated to a set of players so as to maximize the sum of the utilities of the players (i.e., the social welfare). In the case when the utility of each player is a monotone submodular function, we prove that there is no polynomial time approximation algorithm which approximates the maximum social welfare by a factor better than 1–1/e ≃ 0.632, unless P = NP. Our result is based on a reduction from a multi-prover proof system for MAX-3-COLORING.

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References

  1. Andelman, N., Mansour, Y.: Auctions with budget constraints. In: Hagerup, T., Katajainen, J. (eds.) SWAT 2004. LNCS, vol. 3111, pp. 26–38. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  2. Archer, A., Papadimitriou, C., Talwar, K., Tardos, E.: An approximate truthful mechanism for combinatorial auctions with single parameter agents. In: SODA, pp. 205–214 (2003)

    Google Scholar 

  3. Arora, S., Lund, C., Motwani, R., Sudan, M., Szegedy, M.: Proof verification and hardness of approximation problems. In: FOCS, pp. 14–23 (1992)

    Google Scholar 

  4. Bartal, Y., Gonen, R., Nisan, N.: Incentive compatible multi unit combinatorial auctions. In: TARK, pp. 72–87 (2003)

    Google Scholar 

  5. Blumrosen, L., Nisan, N.: On the computational power of ascending auctions 1: Demand queries. In: ACM Conference on Electronic Commerce (2005)

    Google Scholar 

  6. Cramton, P., Shoham, Y., Steinberg, R. (eds.): Combinatorial Auctions. MIT Press, Cambridge (2005) (forthcoming)

    Google Scholar 

  7. Dobzinski, S., Nisan, N., Schapira, M.: Approximation algorithms for combinatorial auctions with complement-free bidders. In: STOC (2005)

    Google Scholar 

  8. Dobzinski, S., Schapira, M.: An improved approximation algorithm for combinatorial auctions with submodular bidders. Working paper (2005)

    Google Scholar 

  9. Feige, U.: A threshold of lnn for approximating set cover. Journal of the ACM 45(4), 634–652 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  10. Feige, U., Halldorsson, M.M., Kortsarz, G., Srinivasan, A.: Approximating the domatic number. SIAM Journal of Computing 32(1), 172–195 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  11. Feige, U., Kilian, J.: Zero knowledge and the chromatic number. JCSS 57, 187–199 (1998)

    MATH  MathSciNet  Google Scholar 

  12. Holzman, R., Kfir-Dahav, N., Monderer, D., Tennenholtz, M.: Bundling equilibrium in combinatorial auctions. Games and Economic Behavior 47, 104–123 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  13. Lehmann, B., Lehmann, D., Nisan, N.: Combinatorial auctions with decreasing marginal utilities. In: ACM Conference on Electronic Commerce (2001)

    Google Scholar 

  14. Lehmann, D., O’Callaghan, L., Shoham, Y.: Truth revelation in approximately efficient combinatorial auctions. In: ACM Conference on Electronic Commerce (1999)

    Google Scholar 

  15. Lund, C., Yannakakis, M.: On the hardness of approximating minimization problems. Journal of the ACM 41(5), 960–981 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  16. Nisan, N., Segal, I.: The communication requirements of efficient allocations and supporting lindahl prices. To appear in Journal of Economic Theory (2004), preliminary version: http://www.cs.huji.ac.il/~noam/mkts.html

  17. Papadimitriou, C., Yannakakis, M.: Optimization, approximation and complexity classes. Journal of Computer and System Sciences 43, 425–440 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  18. Raz, R.: A parallel repetition theorem. SIAM Journal of Computing 27(3), 763–803 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  19. Sandholm, T.: An algorithm for optimal winner determination in combinatorial auctions. In: IJCAI (1999)

    Google Scholar 

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Authors and Affiliations

  1. Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Subhash Khot, Richard J. Lipton, Evangelos Markakis & Aranyak Mehta

Authors
  1. Subhash Khot
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  2. Richard J. Lipton
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  3. Evangelos Markakis
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  4. Aranyak Mehta
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Editor information

Editors and Affiliations

  1. Department of Computer Science, City University of Hong Kong, Tat Chee Avenue, Kowloon ,, Hong Kong

    Xiaotie Deng

  2. Stanford University, Stanford, CA

    Yinyu Ye

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© 2005 Springer-Verlag Berlin Heidelberg

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Khot, S., Lipton, R.J., Markakis, E., Mehta, A. (2005). Inapproximability Results for Combinatorial Auctions with Submodular Utility Functions. In: Deng, X., Ye, Y. (eds) Internet and Network Economics. WINE 2005. Lecture Notes in Computer Science, vol 3828. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11600930_10

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  • DOI: https://doi.org/10.1007/11600930_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30900-0

  • Online ISBN: 978-3-540-32293-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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