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Simultaneous Single-Item Auctions

  • Kshipra Bhawalkar
  • Tim Roughgarden
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7695)

Abstract

In a combinatorial auction (CA) with item bidding, several goods are sold simultaneously via single-item auctions. We study how the equilibrium performance of such an auction depends on the choice of the underlying single-item auction. We provide a thorough understanding of the price of anarchy, as a function of the single-item auction payment rule.

When the payment rule depends on the winner’s bid, as in a first-price auction, we characterize the worst-case price of anarchy in the corresponding CAs with item bidding in terms of a sensitivity measure of the payment rule. As a corollary, we show that equilibrium existence guarantees broader than that of the first-price rule can only be achieved by sacrificing its property of having only fully efficient (pure) Nash equilibria.

For payment rules that are independent of the winner’s bid, we prove a strong optimality result for the canonical second-price auction. First, its set of pure Nash equilibria is always a superset of that of every other payment rule. Despite this, its worst-case POA is no worse than that of any other payment rule that is independent of the winner’s bid.

Keywords

Nash Equilibrium Combinatorial Auction Price Rule Equilibrium Allocation Pure Nash Equilibrium 
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.

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References

  1. 1.
    Babaioff, M., Lavi, R., Pavlov, E.: Single-value combinatorial auctions and algorithmic implementation in undominated strategies. Journal of the ACM (JACM) 56(1) (2009)Google Scholar
  2. 2.
    Bhawalkar, K., Roughgarden, T.: Welfare guarantees for combinatorial auctions with item bidding. In: ACM Symposium on Discrete Algorithms, pp. 700–709. SIAM, Philadelphia (2011)Google Scholar
  3. 3.
    Blumrosen, L., Nisan, N.: Combinatorial auctions. In: Nisan, N., Roughgarden, T., Tardos, É., Vazirani, V.V. (eds.) Algorithmic Game Theory, ch. 11, pp. 267–300. Cambridge University Press (2007)Google Scholar
  4. 4.
    Boyan, J., Greenwald, A.: Bid determination in simultaneous auctions: An agent architecture. In: Third ACM Conference on Electronic Commerce, pp. 210–212 (2001)Google Scholar
  5. 5.
    Christodoulou, G., Kovács, A., Schapira, M.: Bayesian Combinatorial Auctions. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 820–832. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  6. 6.
    Crampton, P., Shoham, Y., Steinberg, R.: Combinatorial Auctions. MIT Press (2006)Google Scholar
  7. 7.
    Dobzinski, S.: An impossibility result for truthful combinatorial auctions with submodular valuations. In: Proceedings of the 43rd Annual ACM Symposium on Theory of Computing, STOC 2011, pp. 139–148. ACM, New York (2011)Google Scholar
  8. 8.
    Dughmi, S., Roughgarden, T., Yan, Q.: From convex optimization to randomized mechanisms: toward optimal combinatorial auctions. In: STOC, pp. 149–158 (2011)Google Scholar
  9. 9.
    Dughmi, S., Vondrák, J.: Limitations of randomized mechanisms for combinatorial auctions. In: FOCS, pp. 502–511 (2011)Google Scholar
  10. 10.
    Fu, H., Kleinberg, R., Lavi, R.: Conditional equilibrium outcomes via ascending price processes (submission, 2012)Google Scholar
  11. 11.
    Gul, F., Stacchetti, E.: Walrasian equilibrium with gross substitutes. Journal of Economic Theory 87(1), 95–124 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Hassidim, A., Kaplan, H., Mansour, M., Nisan, N.: Non-price equilibria in markets of discrete goods. In: 12th ACM Conference on Electronic Commerce (EC), pp. 295–296. ACM, New York (2011)CrossRefGoogle Scholar
  13. 13.
    Kagel, J.H., Levin, D.: Independent private value auctions: Bidder behaviour in first-, second-, and third-price auctions with varying numbers of bidders. The Economic Journal 103, 868–879 (1993)CrossRefGoogle Scholar
  14. 14.
    Kelso, A.S., Crawford, V.P.: Job matching, coalition formation, and gross substitutes. Econometrica 50, 1483–1504 (1982)zbMATHCrossRefGoogle Scholar
  15. 15.
    Paes Leme, R., Tardos, É.: Pure and Bayes-Nash price of anarchy for generalized second price auction. In: 51st Annual IEEE Symposium on Foundations of Computer Science, FOCS, pp. 735–744 (2010)Google Scholar
  16. 16.
    Leme, R.P., Syrgkanis, V., Tardos, É.: Sequential auctions and externalities. In: Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 869–886 (2012)Google Scholar
  17. 17.
    Lucier, B., Borodin, A.: Price of anarchy for greedy auctions. In: 21st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA, pp. 537–553 (2010)Google Scholar
  18. 18.
    Monderer, D., Tennenholtz, M.: K-price auctions. Games and Economic Behavior 31(2), 220–244 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Monderer, D., Tennenholtz, M.: K-price auctions: Revenue inequalities, utility equivalence, and competition in auction design. Economic Theory 24(2), 255–270 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Syrgkanis, V., Tardos, É.: Bayesian sequential auctions. In: ACM Conference on Electronic Commerce, pp. 929–944 (2012)Google Scholar
  21. 21.
    Yoon, D.Y., Wellman, M.P.: Self-confirming price prediction for bidding in simultaneous second-price sealed-bid auctions. In: IJCAI 2011 Workshop on Trading Agent Design and Analysis (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Kshipra Bhawalkar
    • 1
  • Tim Roughgarden
    • 1
  1. 1.Stanford UniversityStanfordUSA

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