All Nash Equilibria of the Multi-Unit Vickrey Auction∗
نویسندگان
چکیده
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. Journal of Economic Literature Classification Numbers: C72, D44.
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An Experimental Examination of Demand Reduction in Multi-Unit Versions of the Uniform-Price, Vickrey, and English Auctions
Vickrey (1961) provided a game-theoretic analysis of the single-unit second price auction and showed that bidders have an incentive to set their bids equal to their valuations. Groves (1973), Clarke (1971), and Forsythe, Isaac, and Palfrey (1989) generalized this analysis for public goods and multiple unit auctions. The cornerstone of the Vickrey auction is its pricing rule by which the winner'...
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