All Nash Equilibria of the Multi-Unit Vickrey Auction

Andreas Blume, Paul Heidhues (), Jonathan Lafky, Johannes Münster and Meixia Zhang

Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems from Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich

Abstract: This paper completely characterizes the set of Nash equilibria of the Vickrey auction for multiple identical units when buyers have non-increasing marginal valuations and there at least three potential buyers. There are two types of equilibria: In the first class of equilibria there are positive bids below the maximum valuation. In this class, above a threshold value all bidders bid truthfully on all units. One of the bidders bids at the threshold for any unit for which his valuation is below the threshold; the other bidders bid zero in this range. In the second class of equilibria there are as many bids at or above the maximum valuation as there are units. The allocation of these bids is arbitrary across bidders. All the remaining bids equal zero. With any positive reserve price equilibrium becomes unique: Bidders bid truthfully on all units for which their valuation exceeds the reserve price.

Keywords: Vickrey auction; Multi-unit auction; ex-post equilibrium; reserve price; uniqueness (search for similar items in EconPapers)
JEL-codes: C72 D44 (search for similar items in EconPapers)
Date: 2006-06
New Economics Papers: this item is included in nep-gth
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Citations: View citations in EconPapers (1)

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