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

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

Understanding Strategic Bidding in Restructured Electricity Markets: A Case Study of ERCOT

We examine the bidding behavior of firms competing on ERCOT, the hourly electricity balancing market in Texas. We characterize an equilibrium model of bidding into this uniform-price divisible-good auction market. Using detailed firm-level data on bids and marginal costs of generation, we find that firms with large stakes in the market performed close to theoretical benchmarks of static, profit-maximizing bidding derived from our model. However, several smaller firms utilized excessively steep bid schedules that deviated significantly from our theoretical benchmarks, in a manner that could not be empirically accounted for by the presence of technological adjustment costs, transmission constraints, or collusive behavior. Our results suggest that payoff scale matters in firms' willingness and ability to participate in complex, strategic market environments. Finally, although smaller firms moved closer to theoretical bidding benchmarks over time, their bidding patterns contributed to productive inefficiency in this newly restructured market, along with efficiency losses due to the close-to optimal exercise of market power by larger firms.

Using Laboratory Experiments For Policy Making: An Example From The Georgia Irrigation Reduction Auction

In April 2000, the Georgia legislature passed a law requiring that the state use an unspecified "auction-like process" to pay some farmers to suspend irrigation in declared drought years. In response, we conducted a series of laboratory and field experiments to test a variety of auction procedures. This paper reports the results of these experiments, and how they were used by the policy makers who determined the auction procedures. Experimental results are compared with farmers' bidding behavior in the state-run irrigation auction conducted in March 2001. Working Paper # 2002-00

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

Modeling Electricity Auctions

The recent debates over discriminatory versus uniform-price auctions in the UK and elsewhere have revealed an incomplete understanding of the limitations of some popular auction models when applied to real-world electricity markets. This has led certain regulatory authorities to prefer discriminatory auctions on the basis of reasoning from models which are not directly applicable to any existing electricity market. Vickrey auctions, although often recommended by economists, have also been ignored in these debates. This article describes the approach which we believe should be taken to analyzing these issues