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Multiple unit auctions of an indivisible good

Author

Listed:
  • Fernando Branco

    (Universidade CatÕlica Portuguesa, FCEE, Palma de Cima, P-1600 Lisboa, PORTUGAL, and Banco de Portugal, Av. Almirante Reis 71, P-1100 Lisboa, PORTUGAL)

Abstract

This paper studies the properties of several multiple unit auctions in the context of a general model that allows for private values and common values as special cases. The benchmark for the analysis is provided by the characterization of optimal selling procedures for a seller that has several units of a homogeneous indivisible good to be sold extending the analysis of a single unit model in [1]. It is shown that the seller should impose endogenous individual minimum announcements, that are contingent on the bidders' reports and decreasing as the number of units allocated to the buyer increase. Implementation mechanisms are discussed in the context of a special case of the model. Under the assumption of unit demands, it is shown that some generalizations (to multiple units) of standard auctions may implement the optimal mechanism, but some do not. Moreover, it is proven that in a sequential optimal auction the sequence of prices paid in each auction is a supermartingale, which conforms to the empirical behavior of prices in sequential auctions.

Suggested Citation

  • Fernando Branco, 1996. "Multiple unit auctions of an indivisible good," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 77-101.
    • Handle: RePEc:spr:joecth:v:8:y:1996:i:1:p:77-101
    Note: Received: May 9, 1994; revised version May 31, 1995
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    Citations

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    Cited by:

    1. Roberto Burguet, 2000. "Auction theory: a guided tour," Investigaciones Economicas, Fundación SEPI, vol. 24(1), pages 3-50, January.
    2. Nicolas Figueroa & Vasiliki Skreta, 2006. "The Role of Outside Options in Auction Design," Levine's Bibliography 321307000000000140, UCLA Department of Economics.
    3. Csapó, Gergely & Müller, Rudolf, 2013. "Optimal mechanism design for the private supply of a public good," Games and Economic Behavior, Elsevier, vol. 80(C), pages 229-242.
    4. Hitoshi Matsushima, 2012. "Optimal Multiunit Exchange Design," CARF F-Series CARF-F-279, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    5. Hitoshi Matsushima, 2012. "Optimal Multiunit Exchange Design with Single-Dimensionality," CARF F-Series CARF-F-292, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Sep 2012.
    6. Domenico Menicucci, 2003. "Optimal two-object auctions with synergies," Review of Economic Design, Springer;Society for Economic Design, vol. 8(2), pages 143-164, October.
    7. Crémer, Jacques & Hariton, Cyril, 2003. "Rental of a Durable Good," IDEI Working Papers 162, Institut d'Économie Industrielle (IDEI), Toulouse.
    8. Branco, Fernando, 1997. "Sequential auctions with synergies: An example," Economics Letters, Elsevier, vol. 54(2), pages 159-163, February.
    9. Rosen, Christiane & Madlener, Reinhard, 2013. "An Experimental Analysis of Single vs. Multiple Bids in Auctions of Divisible Goods," FCN Working Papers 8/2013, E.ON Energy Research Center, Future Energy Consumer Needs and Behavior (FCN), revised Nov 2013.
    10. Ghosh, Gagan & Liu, Heng, 2021. "Sequential auctions with ambiguity," Journal of Economic Theory, Elsevier, vol. 197(C).
    11. Page Jr., F.H., 1997. "Existence of Optimal Auctions in General Environments," Other publications TiSEM 258e7c42-1fc1-41d2-aafb-4, Tilburg University, School of Economics and Management.
    12. Levent Ulku, 2012. "Nonmonotone Mechanism Design," Working Papers 1202, Centro de Investigacion Economica, ITAM.
    13. Page Jr., Frank H., 1998. "Existence of optimal auctions in general environments," Journal of Mathematical Economics, Elsevier, vol. 29(4), pages 389-418, May.
    14. Lionel Thomas, 2001. "Les marchés à tranches," Recherches économiques de Louvain, De Boeck Université, vol. 67(4), pages 437-451.
    15. Levent Ülkü, 2013. "Optimal combinatorial mechanism design," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(2), pages 473-498, June.
    16. Vijay Krishna & Motty Perry, 1997. "Efficient Mechanism Design," Game Theory and Information 9703010, University Library of Munich, Germany, revised 28 Apr 1998.
    17. Bossert, Walter, 1998. "Welfarism and rationalizability in allocation problems with indivisibilities1," Mathematical Social Sciences, Elsevier, vol. 35(2), pages 133-150, March.
    18. Levent Ülkü, 2014. "Mechanism design without monotone differences: an example featuring buyer habits," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(2), pages 183-195, October.
    19. Lionel THOMAS, 2001. "Les marchés à tranches," Discussion Papers (REL - Recherches Economiques de Louvain) 2001045, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    20. Ülkü, Levent, 2014. "Implementation in an interdependent value framework," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 64-70.
    21. Nicolás Figueroa & Vasiliki Skreta, 2011. "Optimal allocation mechanisms with single-dimensional private information," Review of Economic Design, Springer;Society for Economic Design, vol. 15(3), pages 213-243, September.

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