On the Inefficiency of the Uniform Price Auction

We present our results on Uniform Price Auctions, one of the standard sealed-bid multi-unit auction formats, for selling multiple identical units of a single good to multi-demand bidders. Contrary to the truthful and economically efficient multi-unit Vickrey auction, the Uniform Price Auction encourages strategic bidding and is socially inefficient in general. The uniform pricing rule is, however, widely popular by its appeal to the natural anticipation, that identical items should be identically priced. In this work we study equilibria of the Uniform Price Auction for bidders with (symmetric) submodular valuation functions, over the number of units that they win. We investigate pure Nash equilibria of the auction in undominated strategies; we produce a characterization of these equilibria that allows us to prove that a fraction 1-1/e of the optimum social welfare is always recovered in undominated pure Nash equilibrium -- and this bound is essentially tight. Subsequently, we study the auction under the incomplete information setting and prove a bound of 4-2/k on the economic inefficiency of (mixed) Bayes Nash equilibria that are supported by undominated strategies.Comment: Additions and Improvements upon SAGT 2012 results (and minor corrections on the previous version

Demand Reduction and Inefficiency in Multi-Unit Auctions

Auctions typically involve the sale of many related goods. The FCC spectrum auctions and the Treasury debt auctions are examples. With conventional auction designs, large bidders have an incentive to reduce demand in order to pay less for their winnings. This incentive creates an inefficiency in multi-unit auctions. Large bidders reduce demand for additional units and so sometimes lose to smaller bidders with lower values. We demonstrate this inefficiency in several auction settings: flat demand and downward-sloping demand, independent private values and correlated values, and uniform pricing and pay-your-bid pricing. We also establish that the ranking of the uniform-price and pay-your-bid auctions is ambiguous. We show how a Vickrey auction avoids this inefficiency and how the Vickrey auction can be implemented with a simultaneous, ascending-bid design (Ausubel 1997). Bidding behavior in the FCC spectrum auctions illustrates the incentives for demand reduction and the associated inefficiency.Auctions; Multi-Unit Auctions; Spectrum Auctions; Treasury Auctions

Reducing Inefficiency in Carbon Auctions with Imperfect Competition

We study auctions for carbon licenses, a policy tool used to control the social cost of pollution. Each identical license grants the right to produce a unit of pollution. Each buyer (i.e., firm that pollutes during the manufacturing process) enjoys a decreasing marginal value for licenses, but society suffers an increasing marginal cost for each license distributed. The seller (i.e., the government) can choose a number of licenses to put up for auction, and wishes to maximize the societal welfare: the total economic value of the buyers minus the social cost. Motivated by emission license markets deployed in practice, we focus on uniform price auctions with a price floor and/or price ceiling. The seller has distributional information about the market, and their goal is to tune the auction parameters to maximize expected welfare. The target benchmark is the maximum expected welfare achievable by any such auction under truth-telling behavior. Unfortunately, the uniform price auction is not truthful, and strategic behavior can significantly reduce (even below zero) the welfare of a given auction configuration. We describe a subclass of "safe-price" auctions for which the welfare at any Bayes-Nash equilibrium will approximate the welfare under truth-telling behavior. We then show that the better of a safe-price auction, or a truthful auction that allocates licenses to only a single buyer, will approximate the target benchmark. In particular, we show how to choose a number of licenses and a price floor so that the worst-case welfare, at any equilibrium, is a constant approximation to the best achievable welfare under truth-telling after excluding the welfare contribution of a single buyer

The Efficiency of the FCC Spectrum Auctions

From July 1994 to July 1996, the Federal Communications Commission (FCC) conducted nine spectrum auctions, raising about $20 billion for the U.S. Treasury. The auctions assigned thousands of licenses to hundreds of firms. Were the auctions efficient? Did they award the licenses to the firms best able to turn the spectrum into valuable services for onsumers? There is substantial evidence that the FCC's simultaneous ascending auction worked well. It raised large revenues. It revealed critical information in the process of bidding and gave bidders the flexibility to adjust strategies in response to new information. As a result, similar licenses sold for similar prices, and bidders were able to piece together sensible sets of licenses.Auctions; Multiple-Item Auctions; Spectrum Auctions

Asset Auctions, Information, and Liquidity

A model is presented of a uniform price auction where bidders compete in demand schedules; the model allows for common and private values in the absence of exogenous noise. It is shown how private information yields more market power than the levels seen with full information. Results obtained here are broadly consistent with evidence from asset auctions, may help explain the response of central banks to the crisis, and suggest potential improvements in the auction formats of asset auctions.adverse selection, market power, reverse auctions, bid shading

Simultaneous Ascending Auction

The simultaneous ascending auction has proved to be a successful method of auctioning many related items. Simultaneous sale and ascending bids enable price discovery, which helps bidders build desirable packages of items. Although package bids are not allowed, the auction format does handle mild complementarities well. I examine the auction design and its performance in practice.Auctions, Ascending Auctions, Market Design