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Auction Papers with Abstracts [ without Abstracts ] [ Google Scholar on my auction work ]


"Comments on the RGGI Market Design." Submitted to RGGI, Inc. by ISO New England and NYISO, 15 November 2007.

"The 700 MHz Spectrum Auction: An Opportunity to Protect Competition In a Consolidating Industry" (with Andrzej Skrzypacz and Robert Wilson), submitted to the U.S. Department of Justice, Antitrust Division, 13 November 2007.

"Forward Reliability Markets: Less Risk, Less Market Power, More Efficiency" (with Steven Stoft) Utilities Policy, forthcoming, 2008.

A forward reliability market is presented. The market coordinates new entry through the forward procurement of reliability options—physical capacity bundled with a financial option to supply energy above a strike price. The market assures adequate generating resources and prices capacity from the bids of competitive new entry in an annual auction. Efficient performance incentives are maintained from a load-following obligation to supply energy above the strike price. The capacity payment fully hedges load from high spot prices, and reduces supplier risk as well. Market power is reduced in the spot market, since suppliers enter the spot market with a nearly balanced position in times of scarcity. Market power in the reliability market is addressed by not allowing existing supply to impact the capacity price. The approach, which has been adopted in New England and Colombia, is readily adapted to either a thermal or a hydro system.

"Colombia’s Forward Energy Market," Working Paper, University of Maryland, August 2007. [Presentation, Letter to NordPool]

This paper presents a market design for Colombia’s forward energy market, which is scheduled to began in 2008. The forward energy market is an organized market to procure energy for electricity customers on a forward basis. It includes both the regulated market (residential and other small customers) and the nonregulated market (large customers). Currently, regulated customers represent 68% of the total electricity demand and nonregulated customers represent the remaining 32%. The proposed design is novel in that it integrates both the regulated and nonregulated customers into a single organized market. Although the regulated and nonregulated energy products remain distinct, their integration into a single market facilitates arbitrage between the products, improves liquidity, and reduces transaction costs. Both regulated and nonregulated customers benefit from this unified approach. This paper presents all elements of the market design: the product design (see also Cramton 2007), the auction design, and the transition to the new market.

"Comments on the FCC’s Proposed Competitive Bidding Procedures for Auction 73" (with Gregory Rosston, Andrzej Skrzypacz, and Robert Wilson), 31 August 2007. [Frontline Wireless Filing, Reply Comments]

"An Overview of Combinatorial Auctions" (with Yoav Shoham and Richard Steinberg), ACM SIGecom Exchanges, 7, 3-14, 2007.

An auction is combinatorial when bidders can place bids on combinations of items, called “packages,” rather than just individual items. Computer scientists are interested in combinatorial auctions because they are concerned with the expressiveness of bidding languages, as well as the algorithmic aspects of the underlying combinatorial problem. The combinatorial problem has attracted attention from operations researchers, especially those working in combinatorial optimization and mathematical programming, who are fascinated by the idea of applying these tools to auctions. Auctions have been studied extensively by economists, of course. Thus, the newly emerging field of combinatorial auctions lies at the intersection of computer science, operations research, and economics. In this article, we present a brief introduction to combinatorial auctions, based on our book, Combinatorial Auctions (MIT Press, 2006), in which we look at combinatorial auctions from all three perspectives.

"The Effect of Incumbent Bidding in Set-Aside Auctions: An Analysis of Prices in the Closed and Open Segments of FCC Auction 35" (with Allan T. Ingraham and Hal J. Singer) Telecommunications Policy, 32, 273-290, 2008.

This paper examines the impact of an incumbent carrier’s participation in two simultaneously conducted auctions: one set-aside for non-incumbents and one open to all carriers. This paper estimates the extent to which prices in the closed auction were inflated by the participation of incumbents. This paper also estimates what prices would have been in the open auction had incumbents been excluded from bidding in the closed. It is found that an incumbent’s participation in the closed auction through a front, Alaska Native, enabled it to win more licenses at lower prices in FCC Auction 35. In contrast, non-incumbents won fewer licenses and paid more for what they won. The econometric techniques employed here to estimate prices in a “but for” world could be replicated in future damage analysis. Finally, this paper suggests an alternative method of screening bidders seeking access to set-aside auctions that would be consistent with the FCC’s goal of promoting competition in the wireless industry.

Economist Letter to NTIA on 700 MHz Spectrum Auction (with Andrzej Skrzypacz, Simon Wilkie, and Robert Wilson), 30 July 2007.

As the 700 MHz auction approaches, we are writing to clear up a common misconception about the nature of spectrum auctions and the impact of various rules on auction revenues.

"Essential Entry: Revenues in the 700 MHz Spectrum Auction," Working Paper, University of Maryland, 13 July 2007.

A common misconception is that an open access provision on a sliver of the 700 MHz spectrum would reduce auction revenues. In fact, the open access, wholesale, and bidding credit provisions put forth by Frontline Wireless, will motivate new entry, enhance competition in the auction, and raise revenues.

"Revenues in the 700 MHz Spectrum Auction" (with Andrzej Skrzypacz and Robert Wilson), Working Paper, University of Maryland, 27 June 2007.

There have been several comments that criticize auction rules that prevent the two major low-frequency incumbents from winning all of the newly available spectrum and incorporating it into their proprietary networks. Such rules include new-entrant set-asides, new-entrant bidding credits, and the open access plan. We disagree with these criticisms and argue that given the current market structure, such rules are likely to improve welfare and auction revenues. We are submitting this report to provide sound economic analysis of these claims.

"Economic Comments on the Design of the 700 MHz Spectrum Auction" (with Andrzej Skrzypacz and Robert Wilson), submitted with testimony of James L. Barksdale to the U.S. Senate Committee on Commerce, Science, and Transportation, 14 June 2007. [Initial FCC Filing]

We comment on the service and auction rules discussed in the Report and Order and Further Notice of Proposed Rule Making, FCC 07-72, 27 April 2007. We recommend that the FCC designate one license for a wholesale operation that provides open access nationwide on nondiscriminatory terms. This is necessary to enable entry of new businesses offering wireless services in retail markets. It also enables local operators to offer roaming at competitive prices. The new license accords with the Commission’s policy to encourage competition, and recognizes the benefits to consumers from low prices and expanded services.

"Auction Design for Colombia’s Forward Energy Market," Working Paper, University of Maryland, July 2007. [Presentation]

"Product Design for Colombia’s Regulated Market," Working Paper, University of Maryland, June 2007. [Presentation]

This paper presents a product design for Colombia’s regulated market (MOR), which is scheduled to began in 2008. The regulated market consists of residential and other small customers. Currently, regulated customers represent 69% of the total load. I propose a market based on a single load-following product in which each supplier bids to serve its desired share of the Colombia regulated load. Thus, a supplier that wins a 10% share at auction has an obligation to serve 10% of the actual regulated load in every hour of the commitment period. The supplier is paid the MOR clearing price for every MWh of energy supplied. Deviations between the supplier’s hourly supply and obligation are settled at the spot energy price or the scarcity price, whichever is lower. The spot settlement price is capped at the scarcity price, since the firm energy market provides price coverage for prices above the scarcity price (about US$125/MWh). One-hundred percent of regulated load is purchased on behalf of the regulated customers in a sequence of auctions. Thus, MOR together with the firm energy market provides 100% price coverage for all regulated customers. MOR provides price coverage from zero to the scarcity price, and the firm energy market provides price coverage above the scarcity price. This accomplishes two things: 1) it provides rate stability for regulated customers, and 2) it provides revenue stability for suppliers. The result is reduced risk for both sides of the market.

"Market-Based Alternatives for Managing Congestion at New York’s LaGuardia Airport," (with Michael O. Ball, Lawrence M. Ausubel, Frank Berardino, George Donohue, Mark Hansen, and Karla Hoffman), in Optimal Use of Scarce Airport Capacity, Proceedings of AirNeth Annual Conference, The Hague, April 2007.

We summarize the results of a project that was motivated by the expiration of the “High Density Rule,” which defined the slot controls employed at New York’s LaGuardia Airport for more than 30 years. The scope of the project included the analysis of several administrative measures, congestion pricing options and slot auctions. The research output includes a congestion pricing procedure and also the specification of a slot auction mechanism. The research results are based in part on two strategic simulations. These were multi-day events that included the participation of airport operators, most notably the Port Authority of New York and New Jersey, FAA and DOT executives, airline representatives and other members of the air transportation community. The first simulation placed participants in a stressful, high congestion future scenario and then allowed participants to react and problem solve under various administrative measures and congestion pricing options. The second simulation was a mock slot auction in which participants bid on LGA arrival and departure slots for fictitious airlines.

"Colombia Firm Energy Market," (with Steven Stoft), Proceedings of the Hawaii International Conference on System Sciences, January 2007.

A firm energy market for Colombia is presented. Firm energy—the ability to provide energy in a dry period—is the product needed for reliability in Colombia’s hydro-dominated electricity market. The firm energy market coordinates investment in new resources to assure that sufficient firm energy is available in dry periods. Load procures in an annual auction enough firm energy to cover its needs. The firm energy product includes both a financial call option and the physical capability to supply firm energy. The call option protects load from high spot prices and improves the performance of the spot market during scarcity. The market provides strong performance incentives through the spot energy price. Market power is addressed directly: existing resources cannot impact the firm energy price. Since load is hedged from high spot prices, the market can rely on high prices to balance supply and demand during dry periods, rather than rationing.

"Simulation of the Colombian Firm Energy Market," (with Steven Stoft and Jeffrey West), Working Paper, University of Maryland, December 2006.

We present a simulation analysis of the proposed Colombian firm energy market. The main purpose of the simulation is to assess the risk to suppliers of participation in the market. We also are able to consider variations in the market design, and assess the impact of alternative auction parameters. Three simulation models are developed and analyzed. The first model (Model 1) uses historical price data from October 1995 through May 2006 to assess the performance risk of hypothetical thermal and hydro generating units. The second model (Model 2) uses historical price and operating data to assess performance risk of the actual generating units in Colombia over the same period. This analysis allows us to assess company risk. The third model (Model 3) differs from the other models in that it explicitly models the firm energy auction and investments going forward. Thus, the model is able to assess how the distribution of firm energy purchases differs from the firm energy target, and how this distribution depends on the firm energy demand curve. Model 3 also studies the investment decisions of suppliers, the impact of lumpy investments, and the impact of a higher scarcity price. Taken together, the simulation results demonstrate the risk reducing benefits of the firm energy market. Provided there is competitive new entry in response to load growth, the firm energy market should work well at coordinating investment in new supply, while minimizing supplier and consumer risks.

"Spectrum Auction Design," Working Paper, University of Maryland, April 2007. [Presentation]

Spectrum auctions are used by governments to assign and price licenses for wireless communication. 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. I then present a variation, the package clock auction, which addresses many of the problems of the simultaneous ascending auction while building on its strengths. The package clock auction is a simple dynamic auction in which bidders bid on packages of lots. Most importantly, the pricing rule and information policy are carefully tailored to mitigate gaming behavior. Truthful bidding is encouraged, which simplifies bidding and improves efficiency.

"Why We Need to Stick with Uniform-Price Auctions in Electricity Markets," (with Steven Stoft), Electricity Journal, 20:1, 26-37, 2007.

Wholesale electricity markets are commonly organized around a spot energy market. Buyers and suppliers submit bids and offers for each hour and the market is cleared at the price that balances supply and demand. Buyers with bids above the clearing price pay that price, and suppliers with offers below the clearing price are paid that same price. This uniform-price auction, which occurs both daily and throughout the day, is complemented by forward energy markets. In practice, between 80 and 95 percent of wholesale electricity is traded in forward energy markets, often a month, or a year, and sometimes many years ahead of the spot market. However, because forward prices reflect spot prices, in the long run, the spot market determines the total cost of energy. It also plays a critical role in the least-cost scheduling and dispatch of resources, and provides an essential price signal both for short-run performance and long-run investment incentives. Arguments that the uniform-price auction yields electricity prices that are systematically too high are incorrect. However, insufficiently hedged spot prices will result in energy costs that fluctuate above and below the long-run average more than regulated prices and more than is socially optimal. Tampering with the spot price would cause inefficiency and raise long-term costs. The proper way to dampen the impact of spot price fluctuations is with long-term hedging. Although re-regulation can provide a hedge, there are less costly approaches.

"The Convergence of Market Designs for Adequate Generating Capacity," (with Steven Stoft), Working Paper, University of Maryland, April 2006.

This paper compares market designs intended to solve the resource adequacy (RA) problem, and finds that, in spite of rivalrous claims, the most advanced designs have nearly converged. The original dichotomy between approaches based on long-term energy contracts and those based on short-term capacity markets spawned two design tracks. Long-term contracts led to call-option obligations which provide market-power control and the ability to strengthen performance incentives, but this approach fails to replace the missing money at the root of the adequacy problem. Hogan’s energy-only market fills this gap. On the other track, the short-term capacity markets (ICAP) spawned long-term capacity market designs. In 2004, ISO New England proposed a short-term market with hedged performance incentives essentially based on high spot prices. In 2005 we developed for New England a forward capacity market with load obligated to purchase a target level of capacity covered by an energy call option. The two tracks have now converged on two conclusions: (1) High real-time energy prices should provide performance incentives. (2) High energy prices should be hedged with call options. We argue that two more conclusions are needed: (3) Capacity targets rather than high and volatile spot prices should guide investment, and (4) long-term physically based options should be purchased in a forward market for capacity. The result will be that adequacy is maintained, performance incentives are restored, market power and risks are reduced from present levels, and prices are hedged down to a level below the present price cap.

Combinatorial Auctions, (with Yoav Shoham and Richard Steinberg) MIT Press, 2006.

A comprehensive book on combinatorial auctions―auctions in which bidders can bid on packages of items. The book consists of original material intended for researchers, students, and practitioners of auction design. It includes a foreword by Vernon Smith, an introduction to combinatorial auctions, and twenty-three cross-referenced chapters in five parts. Part I covers mechanisms, such as the Vickrey auction and the ascending proxy auction. Part II is on bidding and efficiency issues. Part III examines computational issues and algorithmic considerations, especially the winner determination problem―how to identify the (tentative) winning set of bids that maximizes revenue. Part IV discusses implementation and methods of testing the performance of combinatorial auctions, including simulation and experiment. Part V considers four important applications: airport runway access, trucking, bus routes, and industrial procurement. The chapters develop and apply a unified language, integrating ideas from economics, operations research, and computer science. A glossary defines the central terms. The contributors are Lawrence Ausubel, Michael Ball, Martin Bichler, Sushil Bikhchandani, Craig Boutilier, Estelle Cantillon, Chris Caplice, Peter Cramton, Andrew Davenport, George Donohue, Karla Hoffman, Gail Hohner, Jayant Kalagnanam, Ailsa Land, Daniel Lehmann, Kevin Leyton-Brown, Dinesh Menon, Paul Milgrom, Rudolf Müller, Noam Nisan, Eugene Nudelman, Joseph Ostroy, David Parkes, Aleksandar Pekec, Martin Pesendorfer, Susan Powell, Amir Ronen, Michael Rothkopf, Tuomas Sandholm, Ilya Segal, Yossi Sheffi, Yoav Shoham, Richard Steinberg, Susara van den Heever, Thomas Wilson, and Makoto Yokoo.

"Introduction to Combinatorial Auctions," (with Yoav Shoham and Richard Steinberg) in Peter Cramton, Yoav Shoham, and Richard Steinberg (eds.), Combinatorial Auctions, 1-13, MIT Press, 2006.

Combinatorial auctions are those auctions in which bidders can place bids on combinations of items, called “packages,” rather than just individual items. The study of combinatorial auctions is inherently interdisciplinary. Combinatorial auctions are in the first place auctions, a topic extensively studied by economists. Package bidding brings in operations research, especially techniques from combinatorial optimization and mathematical programming. Similarly, computer science is concerned with expressiveness of various bidding languages, and algorithmic aspects of the combinatorial problem. The study of combinatorial auctions thus lies at the intersection of economics, operations research, and computer science. In this book, we look at combinatorial auctions from all three perspectives. Indeed, our contribution is to do so in an integrated and comprehensive way. The first challenge in interdisciplinary research is getting the different disciplines to speak the same language. We have made an effort to use terms consistently throughout the book, with the most common terms defined in the glossary.

"The Clock-Proxy Auction: A Practical Combinatorial Auction Design," (with Lawrence M. Ausubel and Paul Milgrom) in Peter Cramton, Yoav Shoham, and Richard Steinberg (eds.), Combinatorial Auctions, Chapter 5, 115-138, MIT Press, 2006. [Presentation]

We propose the clock-proxy auction as a practical means for auctioning many related items. A clock auction phase is followed by a last-and-final proxy round. The approach combines the simple and transparent price discovery of the clock auction with the efficiency of the proxy auction. Linear pricing is maintained as long as possible, but then is abandoned in the proxy round to improve efficiency and enhance seller revenues. The approach has many advantages over the simultaneous ascending auction. In particular, the clock-proxy auction has no exposure problem, eliminates incentives for demand reduction, and prevents most collusive bidding strategies.

"Simultaneous Ascending Auctions," in Peter Cramton, Yoav Shoham, and Richard Steinberg (eds.), Combinatorial Auctions, Chapter 4, 99-114, MIT Press, 2006.

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.

"Dynamic Auctions in Procurement," (with Lawrence M. Ausubel) in Nicola Dimitri, Gustavo Piga, and Giancarlo Spagnolo (eds.) Handbook of Procurement, Cambridge, England: Cambridge University Press, 2006.

We study the theory and practical implementation of dynamic procurement auctions. We consider the procurement of many related items. With many related items, price discovery is important not only to reduce the winner’s curse, but more importantly, to simplify the bidder’s decision problem and to facilitate the revelation of preferences in the bids. Three auction formats are considered: simultaneous descending auctions are preferred if the items are not divisible, simultaneous clock auctions are desirable for procuring many divisible goods, and the clock-proxy auction is best if complementarities among items are strong and varied across the suppliers. We examine the properties of these auctions and discuss important practical considerations in applying them.

"How Best to Auction Oil Rights," in Macartan Humphreys, Jeffrey D. Sachs, Joseph E. Stiglitz (eds.), Escaping the Resource Curse, Chapter 5, 114-151, New York: Columbia University Press, 2007.

I study the design of oil rights auctions. A good auction design promotes both an efficient assignment of rights and competitive revenues for the seller. The structure of bidder preferences and the degree of competition are key factors in determining the best design. With weak competition and additive values, a simultaneous first-price sealed-bid auction may suffice. With more complex value structures, a dynamic auction with package bids, such as the clock-proxy auction, likely is needed to promote the efficiency and revenue objectives. Bidding on production shares, rather than bonuses, typically increases government take by reducing oil company risk.

"New England’s Forward Capacity Auction," University of Maryland, June 2006.

This note provides a brief description of New England’s Forward Capacity Auction (FCA) for the procurement of electricity capacity. The description is based on the 6 March 2006 Settlement Agreement. The description here presents a simpler description of the auction mechanics, and limits the presentation to the key elements relevant to someone providing software and other support to implement the primary auction. In addition, some motivation for the approach is given. The description here is not a software specification, but rather a high-level description of the auction. Many implementation details are yet to be resolved. These details will be resolved in the Market Rule for the Forward Capacity Market.

"A Capacity Market that Makes Sense," (with Steven Stoft) Electricity Journal, 18, 43-54, August/September 2005. [Presentation]

We argue that a capacity market is needed in most restructured electricity markets, and present a design that avoids problems found in the early capacity markets. The proposed market only rewards capacity that contributes to reliability as demonstrated by its performance during hours in which there is a shortage of operating reserves. The capacity price responds to market conditions, increasing when and where capacity is scarce and decreasing to zero when and where it is sufficiently plentiful. Market power in the capacity market is addressed by basing the capacity price on actual capacity, rather than bid capacity, so generators cannot increase the capacity price by withholding supply. Actual peak energy rents (the short-run energy and reserve profits of a benchmark peaking unit) are subtracted from the capacity price. This allows the capacity market to more accurately control short-run profits and suppresses market power in the energy market. This design both avoids and hedges energy market risk, and by suppressing market power avoids regulatory risk. Risk reduction saves consumers money as do the performance and investment incentives inherent in the pay-for-performance mechanism.

"Review of the Proposed Reserve Markets in New England," (with Hung-po Chao and Robert Wilson) White Paper, Market Design Inc., January 2005.

ISO New England proposes reserve markets designed to improve the existing forward reserve market and improve pricing during real-time reserve shortages. We support all of the main elements of the proposal. For example, we agree that little is gained by allowing reserve availability bids in the day-ahead market. Doing so greatly increases the complexity of the market without the prospect of more efficient pricing. Rather, offline reserves are most efficiently priced and awarded well in advance, as is done by the improved forward reserve market.

"Auctioning Many Divisible Goods," (with Lawrence M. Ausubel) Journal of the European Economic Association, 2, 480-493, April-May 2004.

We study the theory and practical implementation of auctioning many divisible goods. With multiple related goods, price discovery is important not only to reduce the winner’s curse, but more importantly, to simplify the bidder’s decision problem and to facilitate the revelation of preferences in the bids. Simultaneous clock auctions are especially desirable formats for auctioning many divisible goods. We examine the properties of these auctions and discuss important practical considerations in applying them.

"Competitive Bidding Behavior in Uniform-Price Auction Markets," Proceedings of the Hawaii International Conference on System Sciences, January 2004.

Profit-maximizing bidding in uniform price auction markets involves bidding above marginal cost. It therefore is not surprising that such behavior is observed in electricity markets. This incentive to bid above marginal cost is not the result of coordinated action among the bidders. Rather, each bidder is independently selecting its bid to maximize profits based on its estimate of the residual demand curve it faces. The supplier bids a price for its energy capacity to optimize its marginal tradeoff between higher prices and lower quantities. Price response from either demand or other suppliers prevents the supplier from raising its bid too much. Profit maximizing bidding should be expected and encouraged by regulators. It is precisely this profit maximizing behavior that guides the market toward long-run efficient outcomes.

"Vickrey Auctions with Reserve Pricing," (with Lawrence M. Ausubel) Economic Theory, 23, 493-505, April 2004. Reprinted in Charalambos Aliprantis, et al. (eds.), Assets, Beliefs, and Equilibria in Economic Dynamics, Berlin: Springer-Verlag, 355-368, 2003.

We generalize the Vickrey auction to allow for reserve pricing in a multi-unit auction with interdependent values. In the Vickrey auction with reserve pricing, the seller determines the quantity to be made available as a function of the bidders’ reports of private information, and then efficiently allocates this quantity among the bidders. Truthful bidding is a dominant strategy with private values and an ex post equilibrium with interdependent values. If the auction is followed by resale, then truthful bidding remains an equilibrium in the auction-plus-resale game. In settings with perfect resale, the Vickrey auction with reserve pricing maximizes seller revenues.

"Competitive Bidding Behavior in Uniform-Price Auction Markets," Report before the Federal Energy Regulatory Commission, March 2003.

Profit-maximizing bidding in uniform price auction markets involves bidding above marginal cost. It therefore is not surprising that such behavior is observed in electricity markets. Common bidding behavior such as “hockey stick” bids easily are explained by suppliers determining their supply offers to maximize profits. This incentive to bid above marginal cost is not the result of coordinated action among the bidders. Rather, each bidder is independently selecting its bid to maximize profits based on its estimate of the residual demand curve it faces. Profit-maximizing bidding does not mean that “the sky’s the limit.” Typically, bidders are limited in how high they want to bid. As prices increase, operators become increasingly concerned that their capacity will not be selected—that someone else will step in front of them in the merit order. Only when (1) demand does not respond to price, and (2) the largest unhedged block of capacity is essential to meet demand can the bidder holding this largest block profitably name any price. In all other cases, the supplier bids a price for its energy capacity to optimize its marginal tradeoff between higher prices and lower quantities. Price response from either demand or other suppliers prevents the supplier from raising its bid too much. Profit maximizing bidding should be expected and encouraged by regulators. It is precisely this profit maximizing behavior that guides the market toward long-run efficient outcomes.

"Electricity Market Design: The Good, the Bad, and the Ugly," Proceedings of the Hawaii International Conference on System Sciences, January, 2003.

This paper examines principles of market design as applied to electricity markets. I illustrate the principles with examples of both good and bad designs. I discuss one of the main design challenges—dealing with market power. I then discuss FERC’s choice of a standard market design.

"Collusive Bidding in the FCC Spectrum Auctions," (with Jesse Schwartz) Contributions to Economic Analysis & Policy, 1:1, www.bepress.com/bejeap/contributions/vol1/iss1/art11, 2002.  [Presentation]

This paper describes the signaling that occurred in many of the FCC spectrum auctions. The FCC's simultaneous ascending auctions allowed bidders to bid on numerous communication licenses simultaneously, with bidding remaining open on all licenses until no bidder was willing to raise the bid on any license. Simultaneous open bidding allowed bidders to send messages to their rivals, telling them on which licenses to bid and which to avoid. This "code bidding" occurs when one bidder tags the last few digits of its bid with the market number of a related license. Such bids can help bidders coordinate a division of the licenses, and enforce the proposed division through targeted punishments. Often the meaning of a bid is clear without attaching a market number in the trailing digits. Such a "retaliating bid" need not end in a market number to warn off a rival from a contested market. We examine how extensively bidders signaled each other with retaliating bids and code bids in the DEF-block PCS spectrum auction held from August 1996 through January 1997. We find that only a small fraction of the bidders commonly used these signals. The price differences between those markets where signaling did and did not occur were negligible. However, bidders that used these collusive bidding strategies won more than 40% of the spectrum for sale and paid significantly less for their overall winnings, suggesting that the indirect losses from code bidding and retaliation may be large.

"Demand Reduction and Inefficiency in Multi-Unit Auctions," (with Lawrence M. Ausubel) Working Paper, University of Maryland, July 2002. [Presentation]

Auctions typically involve the sale of many related goods. Treasury, spectrum and electricity auctions are examples. In auctions where bidders pay the market-clearing price for items won, large bidders have an incentive to reduce demand in order to pay less for their winnings. This incentive creates an inefficiency in multiple-item auctions. Large bidders reduce demand for additional items and so sometimes lose to smaller bidders with lower values. We demonstrate this inefficiency in an auction model which allows interdependent values. We also establish that the ranking of the uniform-price and pay-as-bid auctions is ambiguous in both revenue and efficiency terms. Bidding behavior in spectrum auctions, electricity auctions, and experiments highlights the empirical importance of demand reduction.

"Spectrum Auctions," in Martin Cave, Sumit Majumdar, and Ingo Vogelsang, eds., Handbook of Telecommunications Economics, Amsterdam: Elsevier Science B.V., Chapter 14, 605-639, 2002.

Auctions have emerged as the primary means of assigning spectrum licenses to companies wishing to provide wireless communication services. Since July 1994, the Federal Communications Commission (FCC) has conducted 33 spectrum auctions, assigning thousands of licenses to hundreds of firms. Countries throughout the world are conducting similar auctions. I review the current state of spectrum auctions. Both the design and performance of these auctions are addressed.

"Tradeable Carbon Permit Auctions: How and Why to Auction Not Grandfather," (with Suzi Kerr) Energy Policy, 30, 333-345, 2002.

An auction of carbon permits is the best way to achieve carbon caps set by international negotiation to limit global climate change. To minimize administrative costs, permits would be required at the level of oil refineries, natural gas pipe lines, liquid sellers, and coal processing plants. To maximize liquidity in secondary markets, permits would be fully tradable and bankable. The government would conduct quarterly auctions. A standard ascending-clock auction in which price is gradually raised until there is no excess demand would provide reliable price discovery. An auction is preferred to grandfathering (giving polluters permits in proportion to past pollution), because it allows reduced tax distortions, provides more flexibility in distribution of costs, provides greater incentives for innovation, and reduces the need for politically contentious arguments over the allocation of rents.

"Pricing in the California Power Exchange Electricity Market: Should California Switch from Uniform Pricing to Pay-as-Bid Pricing?" (with Alfred E. Kahn, Robert H. Porter, and Richard D. Tabors), Blue Ribbon Panel Report, California Power Exchange, January 2001.

"Uniform Pricing or Pay-as-Bid Pricing: A Dilemma for California and Beyond," (with Alfred E. Kahn, Robert H. Porter, and Richard D. Tabors), Electricity Journal, 70-79, July 2001.

Any belief that a shift from uniform to as-bid pricing would provide power purchasers substantial relief from soaring prices is simply mistaken. The immediate consequence of its introduction would be a radical change in bidding behavior that would introduce new inefficiencies, weaken competition in new generation, and impede expansion of capacity.

"How Affirmative Action at the FCC Auctions Decreased the Deficit," (with Ian Ayres) in Ian Ayres, ed., Pervasive Prejudice? Unconventional Evidence of Race and Gender Discrimination, Chicago: University of Chicago Press, 315-395, 2001. 

"A Review of Markets for Clean Air: The U.S. Acid Rain Program," Journal of Economic Literature, 38, 627-633, September 2000.

"Eliminating the Flaws in New England's Reserve Markets," (with Jeffrey Lien) Working Paper, University of Maryland, March 2000. [Presentation]

"Review of the Reserves and Operable Capability Markets: New England's Experience in the First Four Months," White Paper, Market Design Inc., November 1999. [Figures and Tables | Presentation]

I review the performance of the operating reserves and the operable capability markets in New England. The review covers the first four months of operation from May 1 to August 31, 1999. The review is based on my knowledge of the market rules and their implementation by the ISO, and the market data during this period, including bidding, operating, and settlement information. In the review, I (1) identify the potential market flaws with these markets, (2) look at the performance of the markets to see if the potential problems have materialized, (3) evaluate the ISO's short-term remedies for these market flaws, and (4) propose alternative medium-term solutions to the identified problems. I find that the OpCap and reserve markets have serious flaws that must be addressed. The ISO's short-term fixes have been necessary and effective at addressing the immediate problems. However, better solutions can be adopted in the medium term. In particular, I recommend (1) eliminate the OpCap market, (2) establish a downward sloping demand curve for reserves, (3) pay the clearing price to all resources that provide the service, (4) establish the true real-time supply curve as simply the quantity of the resource made available in real time, (5) establish back down bids in the TMSR market (bids would be infrequent, perhaps monthly), (6) never set a price in the TMSR market less than the largest lost opportunity cost, (7) continue to cascade the quantities of the bids between operating reserve products, and (8) correct the classification of off-line units that provide a service that looks and acts like TMSR. All of these changes are consistent with the long-term solutions proposed for NEPOOL. These changes represent an important step toward the long-term solution involving multi-settlement energy and reserve markets. These markets should be designed carefully to address the basic economic and engineering issues necessary for an efficient wholesale electricity market.

"Collusive Bidding: Lessons from the FCC Spectrum Auctions," (with Jesse Schwartz) Journal of Regulatory Economics, 17, 229-252, May 2000.

The Federal Communications Commission (FCC) spectrum auctions use a simultaneous ascending auction design. Bidders bid on numerous communication licenses simultaneously, with bidding remaining open on all licenses until no bidder is willing to bid higher on any license. With full revelation of bidding information, simultaneous open bidding allows bidders to send messages to their rivals, telling them on which licenses to bid and which to avoid. These strategies can help bidders coordinate a division of the licenses, and enforce the proposed division by directed punishments. We explore the extent that bidders signaled each other with retaliating bids in recent FCC spectrum auctions. These strategies were used frequently by a small fraction of the bidders, and were sometimes effective. Direct estimates of revenue losses from these practices are inconclusive; however, bidders that used these collusive bidding strategies paid significantly less, suggesting that the indirect losses may be much larger. We examine solutions to mitigate collusive bidding in the spectrum auctions, and then apply these ideas to the design of daily electricity auctions.

"The Optimality of Being Efficient," (with Lawrence M. Ausubel) Working Paper, University of Maryland, March 2001. [Presentation]

In an optimal auction, a revenue-optimizing seller often awards goods inefficiently, either by placing them in the wrong hands or by withholding goods from the market. This conclusion rests on two assumptions: (1) the seller can prevent resale among bidders after the auction; and (2) the seller can commit to not sell the withheld goods after the auction. We examine how the optimal auction problem changes when these assumptions are relaxed. In sharp contrast to the no resale assumption, we assume perfect resale: all gains from trade are exhausted in resale. In a multiple object model with independent signals, we characterize optimal auctions with resale. We prove generally that with perfect resale, the seller's incentive to misassign goods is destroyed. Moreover, with discrete types, any misassignment of goods strictly lowers the seller's revenue from the optimum. In auction markets followed by perfect resale, it is optimal to assign goods to those with the highest values.

"The Role of the ISO in U.S. Electricity Markets: A Review of Restructuring in California and PJM," (with Lisa Cameron) Electricity Journal, 71-81, April 1999.

Several regions of the U.S. have sought to restructure the electric power industry by separating the potentially competitive generation sector from the natural monopoly functions of electricity transmission and distribution. Under this restructuring scheme, a central authority, which we will refer to as the independent system operator (ISO), is given control over both the transmission system and the spot market for electricity. The ISO's role in managing the spot market is relatively uncontroversial. This is because the spot market takes place in real time and requires continuous physical adjustments to electricity supply and demand subject to complex constraints, such as the need to maintain voltage and frequency within tight bands. Although the ISO's role in managing the spot market is generally accepted, its role in scheduling and pricing generators prior to actual dispatch was hotly debated during the development of California's market and remains a contentious issue. Like other restructured electricity markets, the California market requires generators to be scheduled for operation on a day-ahead basis and allows for adjustments in these day-ahead schedules up to an hour ahead of actual dispatch. However, the California ISO has a minimal role in this scheduling process; almost all scheduling is carried out by a number of competing scheduling coordinators, referred to as SCs. In contrast, the ISO in the Pennsylvania New Jersey Maryland market (PJM) schedules all generators that do not elect to schedule themselves. This paper discusses the California and PJM approaches to shed light on the controversy over the ISO's role in pre-dispatch phases of the market. Section I describes the California market while Section II briefly reviews PJM. Section III outlines the costs and benefits associated with limiting the ISO's role in the scheduling phases of the market. Section IV summarizes recent experience in California and PJM and offers conclusions.

"A Review of ISO New England's Proposed Market Rules," (with Robert Wilson) White Paper, Market Design Inc., September 1998. [Presentation]

This report reviews the proposed rules for restructured wholesale electricity markets in New England. We review the market rules, both individually and collectively, and identify potential problems that might limit the efficiency of these markets. We examine alternatives and identify the key tradeoffs among alternative designs. We believe that the wholesale electricity market in New England can begin on December 1, 1998. However, improvements are needed for long-run success. We have identified four major recommendations:

  • Switch to a multi-settlement system.
  • Introduce demand-side bidding.
  • Adopt location-based transmission congestion pricing, especially for the import/export interfaces.
  • Fix the pricing of the ten minute spinning reserves.

Maryland Auction Conference, May 29-31, 1998.

An important economic development of the 1990s has been the restructuring of infrastructure industries. Throughout the world, markets are replacing monopoly, and private firms are increasingly providing goods and services that once were provided by government. Auctions are playing a major role in this restructuring. Auctions provide an efficient and transparent way for governments to allocate scarce resources, for monopolies to divest their assets, and for services to be traded. Applications are seen in every infrastructure industry: telecommunications (e.g., the FCC spectrum auctions), electric power, natural gas, water, air, and transportation. Treasury auctions are a related application.

In the early 1990s, economists realized that existing auction theory was inadequate for these applications. Although auction theory for the sale of a single item is well developed, each of these applications involves the sale of multiple items, often with value interdependencies among items. In response, there has been a burst of research activity on auctions for multiple items. This work is theoretical, experimental, and empirical.

This conference brings together about forty-five experts in the auction field to present and discuss their research on auctions. The conference mixes theorists, experimentalists, and empiricists. The common core is auctions and a desire to apply auction ideas to these important real-world applications.

"Auctioning Securities," (with Lawrence M. Ausubel) Working Paper, University of Maryland, March 1998.

Treasury debt and other divisible securities are traditionally sold in either a pay-your-bid (discriminatory) auction or a uniform-price auction. We compare these auction formats with a Vickrey auction and also with two ascending-bid auctions. The Vickrey auction and the alternative ascending-bid auction (Ausubel 1996) have important theoretical advantages for sellers. In a setting without private information, these auctions achieve the maximal revenue as a unique equilibrium in dominant strategies. In contrast, the pay-your-bid, uniform-price, and standard ascending-bid auction admit a multiplicity of equilibria that yield low revenues for the seller. We show how these results extend to a setting where bidders have affiliated private information. Our results question the standard ways that securities are offered to the public.

Simultaneous Ascending Auctions with Package Bidding, (with John McMillan, Paul Milgrom, Bradley Miller, Bridger Mitchell, Daniel Vincent, and Robert Wilson) Report to the Federal Communications Commission, March 1998.

An effective package bidding mechanism addresses three problems: the exposure problem (the risks a bidder faces in trying to construct an efficiently large combination of licenses), the free-rider problem (the difficulties small bidders have in beating those who bid for larger packages of licenses), and the computational complexity problem (which arises from the fact that the number of possible combinations of licenses is much larger than the number of licenses). Package bidding offers the possibility of an improvement over individual-license bidding only when there are strong complementarities and the pattern of those complementarities varies across bidders. Package bidding works satisfactorily only when the auction rules have been carefully designed to manage all three problems.

"Efficient Relocation of Spectrum Incumbents," (with Evan Kwerel and John Williams) Journal of Law and Economics, 41, 647-675, October 1998.

Changes in technologies and in consumer demands have made prior radio spectrum allocations far from efficient. To address this problem the FCC has recently reallocated spectrum for more flexible use in bands that are partially occupied by incumbent license holders. Often, it is necessary for the new license holder to relocate incumbents to make efficient use of the spectrum. Regulations structuring the negotiation between incumbent and new entrant can promote efficiency. In particular, giving the new entrant the right to move the incumbent with compensation can reduce negotiation costs and promote efficiency when there is private information about spectrum values but good public information about the cost of relocating the incumbent. We examine the experience of broadband PCS entrants in relocating microwave incumbents. We conclude with some remarks on how these ideas might be applied to digital television spectrum.

"The Distributional Effects of Carbon Regulation," (with Suzi Kerr) in Thomas Sterner (ed.) The Market and the Environment, Cheltenham, United Kingdom: Edward Elgar, chapter 12, 1999.

We examine the distributional effects of carbon regulation. An auction of carbon permits is the best way to achieve carbon caps set by international negotiation to limit global climate change. An auction is preferred to grandfathering (giving polluters permits in proportion to past pollution), because it allows reduced tax distortions, provides more flexibility in distribution of costs, provides greater incentives for innovation, and reduces the need for politically contentious arguments over the allocation of rents.

"Ascending Auctions," European Economic Review, 42:3-5, 745-756, May 1998. [Presentation]

A key question of auction design is whether to use an ascending-bid or a sealed-bid format. The critical distinction between formats is that an ascending auction provides the bidders with information through the process of bidding. This information is a two-edged sword. It may stimulate competition by creating a reliable process of price discovery, by reducing the winner’s curse, and by allowing efficient aggregations of items. Alternatively, the information may be used by bidders to establish and enforce collusive outcomes. Ex ante asymmetries and weak competition favor a sealed-bid design. In other cases, an ascending auction is likely to perform better in efficiency and revenue terms. Moreover, information in an ascending auction can be tailored to limit collusion.

"The Efficiency of the FCC Spectrum Auctions," Journal of Law and Economics, 41, 727-736, October 1998.

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 consumers? 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 and Takeovers," New Palgrave Dictionary of Economics and the Law, Peter Neuman (ed.), London: MacMillan Press, 1, 122-125, 1998.

Under Delaware law (the predominant corporate law in the US), when a potential acquirer makes a serious bid for a target, the target's board of directors is required to act as would "auctioneers charged with getting the best price for the stock-holders at a sale of the company." (Revlon v. MacAndrews & Forbes, 173). The target's board may not use defensive tactics that destroy the auction process and must attempt to seek higher bids. Similarly, the Williams Act requires takeover bids to remain open for at least 20 business days on the grounds that the delay facilitates auctions. This preference for auctions follows from the view that auctions maximize shareholder returns. In addition, auctions promote efficiency by shifting corporate assets into the hands of those that value them most highly. And auctions mitigate the collective action problem of target shareholders by requiring the target board to seek the highest bid. Takeover auctions differ from traditional auctions in important respects. In a traditional auction, the seller describes what is being sold and states the auction rules in a public announcement. Takeover auctions are instead prompted by a potential buyer. Only after the buyer has expressed an interest in the target are bids from others sought. The process is governed not by a fixed set of auction rules specified by the seller, but rather by complex takeover regulations, which give the target board some latitude in the process. The process is typically not stated in advance, but evolves as bidders and bids arrive. For the most part, the regulations provide ways to defend against hostile takeovers with poison pills, greenmail, and other tactics. Despite these differences, to a first approximation takeovers are well modeled as an ascending-bid auction with significant participation costs. This essay begins by looking at takeover auctions from the point of view of a buyer, focusing on bidding strategy. Then strategies of the target are discussed. Finally, the desirability of takeover auctions is addressed.

Package Bidding for Spectrum Licenses, (with John McMillan, Paul Milgrom, Bradley Miller, Bridger Mitchell, Daniel Vincent, and Robert Wilson) Report to the Federal Communications Commission, October 1997.

The FCC was an innovator in adopting the rules of the simultaneous ascending-price auction for its sales of spectrum licenses. While these rules have performed well in the auctions conducted so far (and would perform even better with the design improvements suggested in our first report), there are two inherent limitations in any design that seeks to assign and price the licenses individually. First, such designs create strategic incentives for bidders interested in multiple licenses that are substitutes to reduce their demands for some of the licenses in order to reduce the final prices of the others; this is the demand reduction problem. Second, even if bidders behave non-strategically, there is a fundamental problem with the basic concept of individual-license pricing when licenses are complementary. In simultaneous ascending-price auctions, from a bidder's perspective this is the exposure problem. A bidder who is unsuccessful in bidding for a large package of licenses may be left with a partial package whose total price cannot be justified in the absence of those complementary licenses it failed to win. This problem is present in any auction mechanism that sells licenses individually, with no opportunity to bid on packages. In this report our task is confined to analyses of the merits of package bidding and the practical problems of implementation. In our next report, we will outline proposals for the details of the procedural rules and other aspects of implementing a practical design, as well as the software development that would be necessary.

Auction Design Enhancements for Non-Combinatorial Auctions, (with John McMillan, Paul Milgrom, Bradley Miller, Bridger Mitchell, Daniel Vincent, and Robert Wilson) Report to the Federal Communications Commission, September 1997.

We evaluate a number of possible enhancements to the FCC auctions. We consider only changes to the current auction rules that stay within the basic format of the simultaneous multiple round auction for individual licenses. This report summarizes and extends our e-mail exchanges with FCC staff on this topic. A subsequent report will cover auctions with combination bids. Overall, the FCC spectrum auctions have been an enormous success. However, there are two design goals in the auction where important improvement can be achieved within the basic rules structure. These are restricting collusion among bidders and reducing the time taken to complete the auction. This report focuses on enhancements that help to achieve these two goals. Some of the suggested changes also streamline the auction process so large auctions can be conducted more quickly without sacrificing efficiency.

"The FCC Spectrum Auctions: An Early Assessment," Journal of Economics and Management Strategy, 6:3, 431-495, 1997. Reprinted in Donald L. Alexander (ed.), Telecommunications Policy, Praeger Publishers, 1997.

This paper analyzes six spectrum auctions conducted by the Federal Communications Commission (FCC) from July 1994 to May 1996. These auctions were simultaneous multiple-round auctions in which collections of licenses were auctioned simultaneously. This auction form proved remarkably successful. Similar items sold for similar prices and bidders successfully formed efficient aggregations of licenses. Bidding behavior differed substantially in the auctions. The extent of bidder competition and price uncertainty played an important role in determining behavior. Bidding credits and installment payments also played a major role in several of the auctions.

"Synergies in Wireless Telephony: Evidence from the Broadband PCS Auctions," (with Lawrence M. Ausubel, R. Preston McAfee, and John McMillan) Journal of Economics and Management Strategy, 6:3, 497-527, 1997. [Data]

We examine bid data from the first two broadband PCS spectrum auctions for evidence of value synergies. First, we estimate a benchmark regression for the determinants of final auction prices. Then, we include variables reflecting the extent to which bidders ultimately won or already owned the adjacent wireless properties. Consistent with geographic synergies in an ascending-bid auction, prices were higher when the highest-losing bidder had adjacent licenses. The footprints of winning bidders suggest that they were often successful in realizing these synergies.

"Auction Design for Standard Offer Service," (with Andrew Parece and Robert Wilson) Working Paper, University of Maryland, July 1997. [Auction Rules]

During the transition to a competitive electricity market, when a consumer does not select an electricity provider, who provides service to the customer and at what price? An auction for this "standard offer service" is a market-based way to assign the service responsibility and to determine its price. We explore the design issues in establishing rules for such an auction.

"Using Auctions to Divest Generation Assets," (with Lisa J. Cameron and Robert Wilson) Electricity Journal, 10:10, 22-31, December 1997.

In most states, ratepayers will compensate utilities for their stranded costs. As a result, these costs must be measured as accurately as possible, in a manner that is easily understood by all concerned parties. We describe the options for measuring stranded costs and argue that a simultaneous ascending auction is the best approach.

"Deficit Reduction Through Diversity: How Affirmative Action at the FCC Increased Auction Competition," (with Ian Ayres) Stanford Law Review, 48:4, 761-815, 1996.

In recent auctions for paging licenses, the Federal Communications Commission has granted businesses owned by minorities and women substantial bidding credits. In this article, Professors Ayres and Cramton analyze a particular auction and argue that the affirmative action bidding preferences, by increasing competition among auction participants, increased the government’s revenue by $45 million. Subsidizing the participation of new bidders can induce established bidders to bid more aggressively. The authors conclude that this revenue-enhancing effect does not provide a sufficient constitutional justification for affirmative action—but when such justification is independently present, affirmative actions can cost the government much less than is currently thought.

"Money Out of Thin Air: The Nationwide Narrowband PCS Auction," Journal of Economics and Management Strategy, 4, 267–343, 1995.

The Federal Communications Commission held its first auction of radio spectrum at the Nationwide Narrowband PCS Auction in July 1994. The simultaneous multiple-round auction, which lasted five days, was an ascending bid auction in which all licenses were offered simultaneously. This paper describes the auction rules and how bidders prepared for the auction. The full history of bidding is presented. Several questions for auction theory are discussed. In the end, the government collected $617 million for ten licenses. The auction was viewed by all as a huge success—an excellent example of bringing economic theory to bear on practical problems of allocating scarce resources.

"The Case for Affirmative Auction: From Conscience to Coffers," (with Ian Ayres) New York Times, 21 May 1995, F13.

The Federal Communications Commission’s auction of wireless communication licenses last fall has been criticized as a huge Government giveaway because of the substantial bidding preferences granted to women and minorities. In March, Federal court action delayed the FCC’s June auction until August to consider the legality of similar preferences. But far from being a giveaway, affirmative action actually increased the total amount paid to the Government by about $15 million. Women and minority bidders were granted a 40 percent bidding credit on certain licenses and the right to pay the Government in installments over 10 years at a favorable rate. The combined effect was that these favored bidders only had to pay the Government 50 percent of any winning bid. So how could such subsidies have raised the total auction revenue? The answer is that giving preferences to relatively weak bidders can induce strong bidders to bid higher. The extra revenue the Government gets from the strong bidders can more than offset the subsidy to the weaker bidders.

"Using Auction Theory to Inform Takeover Regulation," (with Alan Schwartz) Journal of Law, Economics, and Organization, 7, 27–53, 1991.

This paper focuses on certain mechanisms that govern the sale of corporate assets. Under Delaware law, when a potential acquirer makes a serious bid for a target, the target’s Board of Directors is required to act as would "auctioneers charged with getting the best price for the stock-holders at a sale of the company.’’ The Delaware courts’ preference for auctions follows from two premises. First, a firm’s managers should maximize the value of their shareholders’ investment in the company. Second, auctions maximize shareholder returns. The two premises together imply that a target’s board should conduct an auction when at least two firms would bid sums that are nontrivially above the target’s prebid market price.

"Dissolving a Partnership Efficiently," (with Robert Gibbons and Paul Klemperer) Econometrica, 55, 615–632, 1987. Reprinted in Paul Klemperer (ed.), The Economic Theory of Auctions, Volume 2, Cheltenham, UK: Edward Elgar, 2000.

Several partners jointly own an asset that may be traded among them. Each partner has a valuation for the asset; the valuations are known privately and drawn independently from a common probability distribution. We characterize the set of all incentive-compatible and interim-individually-rational trading mechanisms, and give a simple necessary and sufficient condition for such mechanisms to dissolve the partnership ex post efficiently. A bidding game is constructed that achieves such dissolution whenever it is possible. Despite incomplete information about the valuation of the asset, a partnership can be dissolved ex post efficiently provided no single partner owns too large a share; this contrasts with Myerson and Satterthwaite’s result that ex post efficiency cannot be achieved when the asset is owned by a single party.

 

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