Analysis of discrete multi-unit, common value auctions: a study of three sealed-bid mechanisms

Joakim Ahlberg

This paper proposes a discrete bidding model for both quantities and pricing. It has a two-unit demand environment where subjects bid for contracts with an unknown redemption value, common to all bidders. Prior to bidding, the bidders receive private signals of information on the (common) value. The value and the signals are drawn from a known discrete affiliated joint distribution. The relevant task for the paper is to compare the equilibrium strategies and the seller’s revenue of three auction formats. We find that, of the three auctionformats below with two players, the discriminatory auction always gives the largest revenue to the seller; both the uniform and the Vickrey auction have zero revenue equilibrium strategies that put them further down in the revenue ranking. In equilibrium, bidders bid the same amount on both items in the discriminatory auction; a phenomenon not noted in either of the other auction formats.

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