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"Auction"
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The VCG Auction in Theory and Practice
2014
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
Demand Reduction and Inefficiency in Multi-Unit Auctions
2014
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
UNDERSTANDING PREFERENCES: \DEMAND TYPES\, AND THE EXISTENCE OF EQUILIBRIUM WITH INDIVISIBILITIES
2019
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
Spectrum Auction Design
2013
Spectrum auctions are used by governments to assign and price licenses for wireless communications. The standard approach is the simultaneous ascending auction, in which many related lots are auctioned simultaneously in a sequence of rounds. I analyze the strengths and weaknesses of the approach with examples from US spectrum auctions. I then present a variation-the combinatorial clock auctionwhich has been adopted by the UK and many other countries, which addresses many of the problems of the simultaneous ascending auction while building on its strengths. The combinatorial clock auction is a simple dynamic auction in which bidders bid on packages of lots. Most importantly, the auction allows alternative technologies that require the spectrum to be organized in different ways to compete in a technologyneutral auction. In addition, the pricing rule and information policy are carefully tailored to mitigate gaming behavior. An activity rule based on revealed preference promotes price and assignment discovery throughout the clock stage of the auction. Truthful bidding is encouraged, which simplifies bidding and improves efficiency. Experimental tests and early auctions confirm the advantages of the approach.
Journal Article