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

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We propose in this paper a discrete bidding model, both on quantities and in 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. Both the value and the signals are drawn from a known discrete affiliated joint distribution. The relevant task for the paper is to compare equilibrium strategies and the seller's revenue between the three auction formats. We find that, among the three auction formats below with two players, the Vickrey auction always gives the most revenue to the seller, where the discriminatory auction becomes second and the uniform auction last. We also find that, in equilibrium, bidders bid the same amount on both items in the discriminatory auction; a phenomenon we do not notice in either of the other two auction formats. There, different amount of demand reduction is encountered.

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