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Bidding Lower with Higher Values in Multi-Object Auction

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  • McAdams, David

Abstract

Multi-object auctions differ in an important way from single-object auctions. When bidders have multi-object demand, equilibria can exist in which bids decrease as values increase! Consider a model with n bidders who receive affiliated one-dimensional types t and whose marginal values are non-decreasing in t and strictly increasing in own type ti. In the first-price auction of a single object, all equilibria are monotone (over the range of types that win with positive probability) in that each bidder's equilibrium bid is non-decreasing in type. On the other hand, some or all equilibria may be non-monotone in many multi-object auctions. In particular, examples are provided for the as-bid and uniform-price auctions of identical objects in which (i) some bidder reduces his bids on all units as his type increases in all equilibria and (ii) symmetric bidders all reduce their bids on some units in all equilibria, and for the as-bid auction of non-identical objects in which (iii) bidders have independent types and some bidder reduces his bids on some packages in all equilibria. Fundamentally, this difference in the structure of equilibria is due to the fact that payoffs fail to satisfy strategic complementarity and/or modularity in these multi-object auctions.

Suggested Citation

  • McAdams, David, 2002. "Bidding Lower with Higher Values in Multi-Object Auction," Working papers 4249-02, Massachusetts Institute of Technology (MIT), Sloan School of Management.
  • Handle: RePEc:mit:sloanp:1599
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    File URL: http://hdl.handle.net/1721.1/1599
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    References listed on IDEAS

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    1. Lawrence M. Ausubel & Peter Cramton & Marek Pycia & Marzena Rostek & Marek Weretka, 2014. "Demand Reduction and Inefficiency in Multi-Unit Auctions," Review of Economic Studies, Oxford University Press, vol. 81(4), pages 1366-1400.
    2. Matthew O. Jackson & Jeroen M. Swinkels, 2005. "Existence of Equilibrium in Single and Double Private Value Auctions," Econometrica, Econometric Society, vol. 73(1), pages 93-139, January.
    3. Philip J. Reny & Shmuel Zamir, 2004. "On the Existence of Pure Strategy Monotone Equilibria in Asymmetric First-Price Auctions," Econometrica, Econometric Society, vol. 72(4), pages 1105-1125, July.
    4. David McAdams, 2006. "Monotone Equilibrium in Multi-Unit Auctions," Review of Economic Studies, Oxford University Press, vol. 73(4), pages 1039-1056.
    5. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
    6. Jeroen M. Swinkels & Wolfgang Pesendorfer, 2000. "Efficiency and Information Aggregation in Auctions," American Economic Review, American Economic Association, vol. 90(3), pages 499-525, June.
    7. Athey, Susan, 2001. "Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Econometrica, Econometric Society, vol. 69(4), pages 861-889, July.
    8. David McAdams, 2004. "Monotone Equilibrium in Multi-Unit Auctions," Econometric Society 2004 North American Summer Meetings 211, Econometric Society.
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    1. McAdams, David, 2002. "Monotone Equilibrium in Multi-Unit Auctions," Working papers 4254-02, Massachusetts Institute of Technology (MIT), Sloan School of Management.

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    Keywords

    Multi-Object; Auctions;

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