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Demand Reduction and Inefficiency in Multi-Unit Auctions
Auctions often involve the sale of many related goods: Treasury, spectrum, and electricity auctions are examples. In multi-unit auctions, bids for marginal units may affect payments for inframarginal units, giving rise to \"demand reduction\" and furthermore to incentives for shading bids differently across units. We establish that such differential bid shading results generically in ex post inefficient allocations in the uniform-price and pay-as-bid auctions. We also show that, in general, the efficiency and revenue rankings of the two formats are ambiguous. However, in settings with symmetric bidders, the pay-as-bid auction often outperforms. In particular, with diminishing marginal utility, symmetric information and linearity, it yields greater expected revenues. We explain the rankings through multi-unit effects, which have no counterparts in auctions with unit demands. We attribute the new incentives separately to multi-unit (but constant) marginal utility and to diminishing marginal utility. We also provide comparisons with the Vickrey auction.
Journal Article
The VCG Auction in Theory and Practice
We describe two auction forms for search engine advertising and present two simple theoretical results concerning i) the estimation of click-through rates and ii) how to adjust the auctions for broad match search. We also describe some of the practical issues involved in implementing a VCG auction.
Journal Article
T-Rex skeleton sold for $6M in auction
A Tyrannosaurus Rex skeleton named Trinity sold for 5.5 million Swiss francs ($6.13 million) in Zurich on April 18, the first such creature ever put on auction in Europe.
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UNDERSTANDING PREFERENCES: \DEMAND TYPES\, AND THE EXISTENCE OF EQUILIBRIUM WITH INDIVISIBILITIES
An Equivalence Theorem between geometric structures and utility functions allows new methods for understanding preferences. Our classification of valuations into \"Demand Types\" incorporates existing definitions (substitutes, complements, \"strong substitutes,\" etc.) and permits new ones. Our Unimodularity Theorem generalizes previous results about when competitive equilibrium exists for any set of agents whose valuations are all of a \"demand type.\" Contrary to popular belief, equilibrium is guaranteed for more classes of purely-complements than of purely-substitutes, preferences. Our Intersection Count Theorem checks equilibrium existence for combinations of agents with specific valuations by counting the intersection points of geometric objects. Applications include matching and coalition-formation, and the \"Product-Mix Auction\" introduced by the Bank of England in response to the financial crisis.
Journal Article