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Limitations of Deterministic Auction Design for Correlated Bidders

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Algorithms – ESA 2013 (ESA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8125))

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Abstract

The seminal work of Myerson (Mathematics of OR 81) characterizes incentive-compatible single-item auctions among bidders with independent valuations. In this setting, relatively simple deterministic auction mechanisms achieve revenue optimality. When bidders have correlated valuations, designing the revenue-optimal deterministic auction is a computationally demanding problem; indeed, Papadimitriou and Pierrakos (STOC 11) proved that it is APX-hard, obtaining an explicit inapproximability factor of 99.95%. In the current paper, we strengthen this inapproximability factor to 57/58 ≈ 98.3%. Our proof is based on a gap-preserving reduction from the problem of maximizing the number of satisfied linear equations in an over-determined system of linear equations modulo 2 and uses the classical inapproximability result of Håstad (J. ACM 01). We furthermore show that the gap between the revenue of deterministic and randomized auctions can be as low as 13/14 ≈ 92.9%, improving an explicit gap of 947/948 ≈ 99.9% by Dobzinski, Fu, and Kleinberg (STOC 11).

This work was supported by the European Social Fund and Greek national funds through the research funding program Thales on “Algorithmic Game Theory”.

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References

  1. Chakrabarty, D., Goel, G.: On the approximability of budgeted allocations and improved lower bounds for submodular welfare maximization and GAP. In: Proceedings of the 49th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 687–696 (2008)

    Google Scholar 

  2. Chen, X., Hu, G., Lu, P., Wang, L.: On the approximation ratio of k-lookahead auction. In: Chen, N., Elkind, E., Koutsoupias, E. (eds.) Internet and Network Economics. LNCS, vol. 7090, pp. 61–71. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  3. Constantin, F., Ito, T., Parkes, D.C.: Online Auctions for Bidders with Interdependent Values. In: Proceedings of the Sixth International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS), pp. 738–740 (2007)

    Google Scholar 

  4. Crémer, J., McLean, R.: Optimal selling strategies under uncertainty for a discriminating monopolist when demands are interdependent. Econometrica 53(2), 345–361 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  5. Crémer, J., McLean, R.: Full extraction of the surplus in bayesian and dominant strategy auctions. Econometrica 56(6), 1247–1257 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  6. Diakonikolas, I., Papadimitriou, C., Pierrakos, G., Singer, Y.: Efficiency-revenue trade-offs in auctions. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds.) ICALP 2012, Part II. LNCS, vol. 7392, pp. 488–499. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  7. Dobzinski, S., Fu, H., Kleinberg, R.: Optimal auctions with correlated bidders are easy. In: Proceedings of the 43rd ACM Symposium on Theory of Computing (STOC), pp. 129–138 (2011)

    Google Scholar 

  8. Esö, P.: An optimal auction with correlated values and risk aversion. Journal of Economic Theory 125(1), 78–89 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  9. Håstad, J.: Some optimal inapproximability results. Journal of the ACM 48(4), 798–859 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  10. Krishna, V.: Auction Theory. Academic Press (2009)

    Google Scholar 

  11. Levin, D., Smith, J.: Optimal Reservation Prices in Auctions. The Economic Journal 106(438), 1271–1283 (1996)

    Article  Google Scholar 

  12. Maskin, E.: Auctions and efficiency. In: Dewatripont, M., Hansen, L.P., Turnovsky, S.J. (eds.) Advances in Economics and Econometrics: Theory and Applications, Eighth World Congress (Econometric Society Monographs), vol. 3, pp. 1–24 (2003)

    Google Scholar 

  13. Milgrom, P., Weber, R.: A theory of auctions and competitive bidding. Econometrica 50(5), 1098–1122 (1982)

    Article  Google Scholar 

  14. Myerson, R.: Optimal auction design. Mathematics of Operations Research 6(1), 58–73 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  15. Nisan, N., Roughgarden, T., Tardos, É., Vazirani, V.V.: Algorithmic Game Theory. Cambridge University Press, New York (2007)

    Book  MATH  Google Scholar 

  16. Papadimitriou, C., Pierrakos, G.: Optimal deterministic auctions with correlated priors. In: Proceedings of the 43rd ACM Symposium on Theory of Computing (STOC), pp. 119–128 (2011)

    Google Scholar 

  17. Ronen, A.: On approximating optimal auctions. In: Proceedings of the 3rd ACM Conference on Electronic Commerce (EC), pp. 11–17 (2001)

    Google Scholar 

  18. Ronen, A., Saberi, A.: On the hardness of optimal auctions. In: Proceedings of the 43rd Symposium on Foundations of Computer Science (FOCS), pp. 396–405 (2002)

    Google Scholar 

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Caragiannis, I., Kaklamanis, C., Kyropoulou, M. (2013). Limitations of Deterministic Auction Design for Correlated Bidders. In: Bodlaender, H.L., Italiano, G.F. (eds) Algorithms – ESA 2013. ESA 2013. Lecture Notes in Computer Science, vol 8125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40450-4_24

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  • DOI: https://doi.org/10.1007/978-3-642-40450-4_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40449-8

  • Online ISBN: 978-3-642-40450-4

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