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A theoretical and empirical investigation of multi-unit auctions with diminishing marginal valuations
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A theoretical and empirical investigation of multi-unit auctions with diminishing marginal valuations
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A theoretical and empirical investigation of multi-unit auctions with diminishing marginal valuations
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Dissertation
A theoretical and empirical investigation of multi-unit auctions with diminishing marginal valuations
1996
Overview
This dissertation contains both a theoretical and empirical analysis of the sale of two objects to multiple bidders where each bidder has a positive valuation for both objects. A variety of selling mechanisms are considered, including discriminatory, uniform price, and sequential auctions. Working within the independent private values paradigm, a downward sloping demand property is imposed on individual bidder valuations by specifying that a bidder's valuation for a first object is no less than his valuation for an additional object. The first two chapters consider games of complete and incomplete information respectively. In both, bidder behavior is derived for each type of auction. Assuming that bidders are following equilibrium strategies, the auctions are ranked in terms of their revenue generating properties. Next, the efficiency of each auction is examined. The character of equilibrium behavior for these multi-unit auctions differs substantially from that in the single object case. Results are obtained, for a certain class of distributions, which show that there is a large amount of shading in low bids in the uniform price auction. It is shown that this shading results in revenue dominance of the discriminatory auction over the uniform price auction. This result is in sharp contrast to that found in Milgrom and Weber's seminal work on auctions. Further, the uniform price auction is the only auction which does not become efficient as the number of bidders grows large. These two results suggest problems with the use of uniform price auctions by the United States Treasury. The final chapter in the dissertation uses the equilibrium behavior derived in the incomplete information game for a sequence of second price auctions. This behavior displays a higher level of shading of first round bids than there would be if there were no subsequent round. Using data from tobacco auctions, the multi-unit demand model is compared to that commonly used in empirical studies of auctions, the unit-supply model. Using maximum likelihood estimation and Vuong's 1989 test for non-nested models, the unit-supply model is rejected in favor of the multi-unit demand model introduced in this dissertation.
