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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.

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File URL: http://hdl.handle.net/1721.1/1599
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Bibliographic Info

Paper provided by Massachusetts Institute of Technology (MIT), Sloan School of Management in its series Working papers with number 4249-02.

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Date of creation: 16 Aug 2002
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Handle: RePEc:mit:sloanp:1599

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Postal: MASSACHUSETTS INSTITUTE OF TECHNOLOGY (MIT), SLOAN SCHOOL OF MANAGEMENT, 50 MEMORIAL DRIVE CAMBRIDGE MASSACHUSETTS 02142 USA

Related research

Keywords: Multi-Object; Auctions;

References

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  1. Athey, S., 1997. "Sigle Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Working papers 97-11, Massachusetts Institute of Technology (MIT), Department of Economics.
  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, 01.
  3. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
  4. David McAdams, 2006. "Monotone Equilibrium in Multi-Unit Auctions," Review of Economic Studies, Oxford University Press, vol. 73(4), pages 1039-1056.
  5. Lawrence M. Ausubel & Peter Cramton, 1995. "Demand Reduction and Inefficiency in Multi-Unit Auctions," Papers of Peter Cramton 98wpdr, University of Maryland, Department of Economics - Peter Cramton, revised 22 Jul 2002.
  6. David McAdams, 2004. "Monotone Equilibrium in Multi-Unit Auctions," Econometric Society 2004 North American Summer Meetings 211, Econometric Society.
  7. Philip J. Reny & Shmuel Zamir, 2002. "On the Existence of Pure Strategy Monotone Equilibria in Asymmetric First-Price Auctions," Discussion Paper Series dp292, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  8. Wolfgang Pesendorfer & Jeroen M. Swinkels, 1996. "Efficiency and Information Aggregation in Auctions," Discussion Papers 1168, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  9. repec:bla:restud:v:73:y:2006:i:4:p:1039-1056 is not listed on IDEAS
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Cited by:
  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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