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Multiple unit auctions of an indivisible good

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  • 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)

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    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.

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    Bibliographic Info

    Article provided by Springer in its journal Economic Theory.

    Volume (Year): 8 (1996)
    Issue (Month): 1 ()
    Pages: 77-101

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    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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    Cited by:
    1. Nicolás Figueroa & Vasiliki Skreta, 2007. "The Role of Outside Options in Auction Design," Documentos de Trabajo 231, Centro de Economía Aplicada, Universidad de Chile.
    2. Levent Ulku, 2009. "Optimal Combinatorial Mechanism Design," Working Papers 0903, Centro de Investigacion Economica, ITAM.
    3. Nicolás Figueroa & Vasiliki Skreta, 2011. "Optimal allocation mechanisms with single-dimensional private information," Review of Economic Design, Springer, vol. 15(3), pages 213-243, September.
    4. Roberto Burguet, 2000. "Auction theory: a guided tour," Investigaciones Economicas, Fundación SEPI, vol. 24(1), pages 3-50, January.
    5. Csapó Gergely & Müller Rudolf, 2012. "Optimal mechanism design for the private supply of a public good," Research Memorandum 038, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    6. 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.
    7. Domenico Menicucci, 2003. "Optimal two-object auctions with synergies," Review of Economic Design, Springer, vol. 8(2), pages 143-164, October.
    8. Page Jr., Frank H., 1998. "Existence of optimal auctions in general environments," Journal of Mathematical Economics, Elsevier, vol. 29(4), pages 389-418, May.
    9. Levent Ulku, 2012. "Nonmonotone Mechanism Design," Working Papers 1202, Centro de Investigacion Economica, ITAM.
    10. 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.
    11. 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.
    12. Vijay Krishna & Motty Perry, 1997. "Efficient Mechanism Design," Game Theory and Information 9703010, EconWPA, revised 28 Apr 1998.
    13. Branco, Fernando, 1997. "Sequential auctions with synergies: An example," Economics Letters, Elsevier, vol. 54(2), pages 159-163, February.
    14. Crémer, Jacques & Hariton, Cyril, 2003. "Rental of a Durable Good," IDEI Working Papers 162, Institut d'Économie Industrielle (IDEI), Toulouse.
    15. Lionel Thomas, 2001. "Les marchés à tranches," Recherches économiques de Louvain, De Boeck Université, vol. 67(4), pages 437-451.
    16. 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).

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