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Combination Bidding in Multi-Unit Auctions


  • Cantillon, Estelle
  • Pesendorfer, Martin


This paper considers the problem of identification and estimation in the first-price multi-unit auction. It is motivated by the auctions of bus routes held in London where bidders submit bids on combinations of routes as well as on individual routes. We show that submitting a combination bid lower than the sum of the bids on the constituent routes does not require cost synergies and can instead serve as a tool to leverage market power across the different routes. As a result, the welfare consequences of allowing combination bidding in the first price auction are ambiguous, and depend on the importance of the cost synergies. We provide conditions for non-parametric identification of the multidimensional private information in the multi-unit first price auction and derive partial identification results when they are not satisfied. We propose an estimation method consisting of two stages: In the first stage, the distribution of bids is estimated parametrically. In the second stage, the (set of) costs and distribution(s) of costs consistent with the observed behavior are inferred based on the first order conditions for optimally chosen bids. We apply the estimation method to data from the London bus routes market. We quantify the magnitude of cost synergies and assess possible efficiency losses arising in this market.

Suggested Citation

  • Cantillon, Estelle & Pesendorfer, Martin, 2007. "Combination Bidding in Multi-Unit Auctions," CEPR Discussion Papers 6083, C.E.P.R. Discussion Papers.
  • Handle: RePEc:cpr:ceprdp:6083

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    References listed on IDEAS

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    Cited by:

    1. Susan Athey & Philip A. Haile, 2006. "Empirical Models of Auctions," NBER Working Papers 12126, National Bureau of Economic Research, Inc.
    2. Tukiainen, Janne, 2008. "Testing for common costs in the City of Helsinki bus transit auctions," International Journal of Industrial Organization, Elsevier, vol. 26(6), pages 1308-1322, November.
    3. Chow, YuenLeng & Yavas, Abdullah, 2008. "Auctions with Positive Synergies: Experimental Evidence," MPRA Paper 12669, University Library of Munich, Germany.
    4. De Silva, Dakshina G. & Jeitschko, Thomas D. & Kosmopoulou, Georgia, 2005. "Stochastic synergies in sequential auctions," International Journal of Industrial Organization, Elsevier, vol. 23(3-4), pages 183-201, April.
    5. Jeremy T. Fox & Patrick Bajari, 2013. "Measuring the Efficiency of an FCC Spectrum Auction," American Economic Journal: Microeconomics, American Economic Association, vol. 5(1), pages 100-146, February.
    6. Lawrence M. Ausubel & Paul Milgrom, 2004. "Ascending Proxy Auctions," Discussion Papers 03-035, Stanford Institute for Economic Policy Research.
    7. Ausubel Lawrence M & Milgrom Paul R, 2002. "Ascending Auctions with Package Bidding," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-44, August.
    8. Park, Sunju & Rothkopf, Michael H., 2005. "Auctions with bidder-determined allowable combinations," European Journal of Operational Research, Elsevier, vol. 161(2), pages 399-415, March.
    9. Patrick Bajari & Stephanie Houghton & Steven Tadelis, 2004. "Bidding for Incompete Contracts," Working Papers 2004.141, Fondazione Eni Enrico Mattei.
    10. Paul Milgrom, 2006. "Package Auctions and Package Exchanges: the 2004 Fisher-Schultz Lecture," Levine's Bibliography 321307000000000131, UCLA Department of Economics.
    11. Farnia, Farnoush & Frayret, Jean-Marc & Beaudry, Catherine & Lebel, Luc, 2015. "Time-based combinatorial auction for timber allocation and delivery coordination," Forest Policy and Economics, Elsevier, vol. 50(C), pages 143-152.
    12. Patrick Bajari & Stephanie Houghton & Steve Tadelis, 2006. "Bidding for Incomplete Contracts: An Empirical Analysis," NBER Working Papers 12051, National Bureau of Economic Research, Inc.
    13. Chernomaz, Kirill & Levin, Dan, 2012. "Efficiency and synergy in a multi-unit auction with and without package bidding: An experimental study," Games and Economic Behavior, Elsevier, vol. 76(2), pages 611-635.
    14. Estelle Cantillon & Martin Pesendorfer, 2006. "Auctioning bus routes: the London experience," ULB Institutional Repository 2013/9003, ULB -- Universite Libre de Bruxelles.

    More about this item


    combinatorial auction; empirical; multi-unit auction; procurement;

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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