Welfare and Rationality Guarantees for the Simultaneous Multiple-Round Ascending Auction

  • Nicolas Bousquet
  • Yang Cai
  • Adrian Vetta
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9470)


The simultaneous multiple-round auction (SMRA) and the combinatorial clock auction (CCA) are the two primary mechanisms used to sell bandwidth. Recently, it was shown that the CCA provides good welfare guarantees for general classes of valuation functions [7]. This motivates the question of whether similar welfare guarantees hold for the SMRA in the case of general valuation functions.

We show the answer is no. But we prove that good welfare guarantees still arise if the degree of complementarities in the bidder valuations are bounded. In particular, if bidder valuations functions are \(\alpha \)-near-submodular then, under truthful bidding, the SMRA has a welfare ratio (the worst case ratio between the social welfare of the optimal allocation and the auction allocation) of at most \((1+\alpha )\). However, for \(\alpha >1\), this is a bicriteria guarantee, to obtain good welfare under truthful bidding requires relaxing individual rationality. We prove this bicriteria guarantee is asymptotically (almost) tight.

Finally, we examine what strategies are required to ensure individual rationality in the SMRA with general valuation functions. First, we provide a weak characterization, namely secure bidding, for individual rationality. We then show that if the bidders use a profit-maximizing secure bidding strategy the welfare ratio is at most \(1+\alpha \). Consequently, by bidding securely, it is possible to obtain the same welfare guarantees as truthful bidding without the loss of individual rationality.


Ascending auctions SMRA Welfare guarantee Individual rationality Near-submodular 


  1. 1.
    Alkalay-Houlihan, C., Vetta, A.: False-name bidding and economic efficiency in combinatorial auctions. In: Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence (AAAI), pp. 2339–2347 (2014)Google Scholar
  2. 2.
    Ausubel, L., Cramton, P.: Auctioning many divisible goods. J. Eur. Econ. Assoc. 2, 480–493 (2004)CrossRefGoogle Scholar
  3. 3.
    Ausubel, L., Cramton, P.: Auction Design for Wind Rights. Report to Bureau of Ocean Energy Management, Regulation and Enforcement (2011)Google Scholar
  4. 4.
    Ausubel, L., Cramton, P., Milgrom, P.: The clock-proxy auction: a practical combinatorial auction design. In: Cramton, P., Shoham, Y., Steinberg, R. (eds.) Combinatorial Auctions, pp. 115–138. MIT Press, Cambridge (2006)Google Scholar
  5. 5.
    Bichler, M., Georee, J., Mayer, S., Shabalin, P.: Spectrum auction design: simple auctions for complex sales. Telecommun. Policy 38(7), 613–622 (2014)CrossRefGoogle Scholar
  6. 6.
    Boodaghians, S., Vetta, A.: The combinatorial world (of auctions) according to GARP. To appear in Proceedings of Symposium in Algorithmic Game Theory (SAGT) (2015)CrossRefGoogle Scholar
  7. 7.
    Bousquet, N., Cai, Y., Hunkenschröder, C., Vetta, A.: On the economic efficiency of the combinatorial clock auction. arxiv, #1507.06495 (2015)Google Scholar
  8. 8.
    Bousquet, N., Cai, Y., Vetta, A.: Welfare and rationality guarantees for the simultaneous multiple-round ascending auction. arxiv, #1510.00295 (2015)Google Scholar
  9. 9.
    Coase, R.: The Federal Communications Commission. J. Law Econ. 2, 1–40 (1959)CrossRefGoogle Scholar
  10. 10.
    Cramton, P.: Simultaneous ascending auctions. In: Cramton, P., Shoham, Y., Steinberg, R. (eds.) Combinatorial Auctions, pp. 99–114. MIT Press, Cambridge (2006)Google Scholar
  11. 11.
    Cramton, P.: Spectrum auction design. Rev. Ind. Organ. 42(2), 161–190 (2013)CrossRefGoogle Scholar
  12. 12.
    Crawford, P., Knoer, E.: Job matching with heterogenous firms and workers. Econometrica 49(2), 437–450 (1981)CrossRefGoogle Scholar
  13. 13.
    Fu, H., Kleinberg, R., Lavi, R.: Conditional equilibrium outcomes via ascending processes with applications to combinatorial auctions with item bidding. In: Proceedings of the Thirteenth Conference on Electronic Commerce (EC), p. 586 (2012)Google Scholar
  14. 14.
    Gul, F., Stacchetti, E.: Walrasian equilibrium with gross substitutes. J. Econ. Theory 87, 95–124 (1999)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Gul, F., Stacchetti, E.: The English auction with differentiated commodities. J. Econ. Theory 92, 66–95 (2000)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Kelso, A., Crawford, P.: Job matching, coalition formation, and gross substitutes. Econometrica 50(6), 1483–1504 (1982)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Klemperer, P.: Auctions: Theory and Practice. Princeton University Press, Princeton (2004)zbMATHGoogle Scholar
  18. 18.
    Lehmann, B., Lehmann, D., Nisan, N.: Combinatorial auctions with decreasing marginal utilities. Games Econ. Behav. 55(2), 270–296 (2006)MathSciNetCrossRefGoogle Scholar
  19. 19.
    McMillan, J.: Selling spectrum rights. J. Econ. Perspect. 8(3), 145–162 (1994)CrossRefGoogle Scholar
  20. 20.
    McMillan, J.: Why auction the spectrum? Telecommun. Policy 3, 191–199 (1994)Google Scholar
  21. 21.
    Milgrom, P.: Putting auction theory to work: the simultaneous ascending auction. J. Polit. Econ. 108, 245–272 (2000)CrossRefGoogle Scholar
  22. 22.
    Milgrom, P.: Putting Auction Theory to Work. Cambridge University Press, Cambridge (2004)CrossRefGoogle Scholar
  23. 23.
    Porter, D., Rassenti, S., Roopnarine, A., Smith, V.: Combinatorial auction design. Proc. Natl. Acad. Sci. U.S.A. 100(19), 11153–11157 (2003)MathSciNetCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsMcGill UniversityMontrealCanada
  2. 2.LIRIS, Ecole Centrale LyonÉcullyFrance
  3. 3.School of Computer ScienceMcGill UniversityMontrealCanada
  4. 4.Department of Mathematics and Statistics, and School of Computer ScienceMcGill UniversityMontrealCanada

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