Bidding Lower with Higher Values in Multi-Object Auctions

23 Pages Posted: 18 Jul 2002

See all articles by David McAdams

David McAdams

Massachusetts Institute of Technology (MIT) - Economics, Finance, Accounting (EFA)

Date Written: June 2002

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, Bidding Lower with Higher Values in Multi-Object Auctions (June 2002). MIT Sloan Working Paper No. 4249-02. Available at SSRN: https://ssrn.com/abstract=317980 or http://dx.doi.org/10.2139/ssrn.317980

David McAdams (Contact Author)

Massachusetts Institute of Technology (MIT) - Economics, Finance, Accounting (EFA) ( email )

77 Massachusetts Avenue
Cambridge, MA 02139-4307
United States
617-253-1306 (Phone)

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