A Generalized Vickrey Auction

In auction environments where bidders have pure private values, the Vickrey auction (Vickrey, 1961) provides a simple mechanism for efficiently allocating homogeneous goods. However, in environments where bidders have interdependent values, the Vickrey auction does not generally yield efficiency. This manuscript defines a "generalized Vickrey auction" which yields efficiency when bidders have interdependent values. Each bidder reports her type to the auctioneer. Given the reports, the auctioneer determines the allocation that maximizes surplus. The payment rule is the following extension of Vickrey auction pricing: a bidder is charged for a given unit that she wins according to valuations evaluated at the minimum signal that she could have reported and still won that unit.

Implications of Auction Theory for New Issues Markets

Imagine attempting to explain to a visitor, from another era or another planet, the economic rationale behind various institutions in the American economy at the start of the 21st century. Few practices seem more difficult to justify to the outsider than the current procedure for the issuance of equity securities. The share price in initial public offerings (IPO’s) often bears little connection to the equating of supply and demand, so that IPO’s are sometimes massively oversubscribed and the share price increases by as much as a factor of five from the offering price to the close of the first day of trading. Shares in these oversubscribed offerings are rationed, not according to willingness to pay, but to favored clients of the underwriting investment banks. Often there is at least the appearance that clients receive their allotments in exchange for returning value to the investment banks in other transactions; and recently there have been allegations that some allotments have been made in exchange for agreements to buy additional shares on the open market after the IPO. While the associated returns foregone by the sellers (i.e., the companies going public) would be easier to justify if the explicit fees for the service were commensurately discounted, the explicit fees charged for IPO’s actually seem quite high, generally a 7% commission on proceeds from the new shares. The main objective of this paper is not to hammer away at the inefficiencies present in the current system of new equity issuance; nor to attempt to explain what prevents the current system from being swept aside. Rather, this paper seeks to draw from new developments in market designâboth theoretical results and new practices in other sectorsâand to highlight alternative procedures that may be best suited to supplement or replace the current flawed system.

Auctions with Heterogeneous Items and Budget Limits

We study individual rational, Pareto optimal, and incentive compatible mechanisms for auctions with heterogeneous items and budget limits. For multi-dimensional valuations we show that there can be no deterministic mechanism with these properties for divisible items. We use this to show that there can also be no randomized mechanism that achieves this for either divisible or indivisible items. For single-dimensional valuations we show that there can be no deterministic mechanism with these properties for indivisible items, but that there is a randomized mechanism that achieves this for either divisible or indivisible items. The impossibility results hold for public budgets, while the mechanism allows private budgets, which is in both cases the harder variant to show. While all positive results are polynomial-time algorithms, all negative results hold independent of complexity considerations

The Optimality of Being Efficient

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.Auctions; Multiple Object Auctions; Resale

Auction Design Critical for Rescue Plan

The Treasury proposes to invest $700 billion in mortgage-related securities to resolve the financial crisis, using market mechanisms such as reverse auctions to determine prices. A well-designed auction process can indeed be an effective tool for acquiring distressed assets at minimum cost to the taxpayer. However, a simplistic process could lead to higher cost and fewer securities purchased. It is critical for the auction process to be designed carefully.Auctions, financial auctions, financial crisis

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

Making Sense of the Aggregator Bank

On Tuesday, 10 February 2009, Treasury Secretary Geithner proposed the aggregator bank (“public-private investment fund”) as a key instrument to resolve the financial crisis (www.financialstability.gov). The Treasury description leaves many issues unanswered. Here we explain how an aggregator bank might operate in practice. We fill in some of the major details so as to enhance the effectiveness of the aggregator bank. In particular, the approach emphasizes transparency and value to the taxpayer, minimizing the need for bank-by-bank negotiations and thereby minimizing the opportunities for the government to play favorites.Auctions, financial auctions, financial crisis

Using Forward Markets to Improve Electricity Market Design

Forward markets, both medium term and long term, complement the spot market for wholesale electricity. The forward markets reduce risk, mitigate market power, and coordinate new investment. In the medium term, a forward energy market lets suppliers and demanders lock in energy prices and quantities for one to three years. In the long term, a forward reliability market assures adequate resources are available when they are needed most. The forward markets reduce risk for both sides of the market, since they reduce the quantity of energy that trades at the more volatile spot price. Spot market power is mitigated by putting suppliers and demanders in a more balanced position at the time of the spot market. The markets also reduce transaction costs and improve liquidity and transparency. Recent innovations to the Colombia market illustrate the basic elements of the forward markets and their beneficial role.Auctions, electricity auctions, market design, forward markets

No Substitute for the 'P'-Word in Financial Rescue

Three months and three-hundred billion dollars of bank rescue efforts have gotten bogged down in a widespread and irrational fear among policymakers: the fear of trying to put a price on banks’ troubled assets. So profound is this fear that the Bush Treasury opted instead for the “suitcase approach,” where large sums of cash were delivered to banks (solvent and insolvent alike) with few strings attached. The government needs to restore the banking sector, while protecting the interests of taxpayers. There is no substitute for the P-word.Auctions, financial auctions, financial crisis

The optimality of being efficient : designing auctions

A cornerstone of the auction literature is the theory of"optimal auctions."'This theory uses mechanism design techniques to characterize, in general settings, the auction that maximizes the seller's expected revenues. One feature of the solution is that typically there is a conflict between the goals of revenue maximization and efficiency. The revenue-optimizing seller often either places goods in hands other than those who value them the most or withholds goods entirely from the market. However, the conclusion that the seller gains by assigning goods inefficiently depends critically on two strong assumptions: (1) the seller can prevent resale among bidders from occurring after the auction; and (2) the seller can commit to not sell the withheld goods after the auction. In this paper, the authors examine how the optimal auction problem changes when one or both of these assumptions are relaxed. This paper is organized as follows. In section 2, the authors establish the seller's general incentive to misassign goods and they identify settings where the optimal auction is efficient. In section 3, they solve two variations on the optimal auction, which recognize the possibility of resale. Section 4 proves that perfect resale destroys the seller's incentive to misassign goods. Section 5 establishes that with perfect resale, any misassignment of goods results in strictly lower seller revenues than the best efficient assignment. In section 6, the paper shows that the Vickrey auction is not distorted by the possibility of resale.International Terrorism&Counterterrorism,Environmental Economics&Policies,Economic Theory&Research,Banks&Banking Reform,Markets and Market Access,Economic Theory&Research,Banks&Banking Reform,Access to Markets,International Terrorism&Counterterrorism,Environmental Economics&Policies