Sequential equilibria of asymmetric ascending auctions: The case of log-normal distributions

Summary. The sequential equilibrium of an ascending-price auction of a single item is derived explicitly for the case of log-normal distributions and a multiplicative valuation model comprising both common and private factors, and allowing asymmetries. If the prior distribution on the common factors is diffuse, or of the form obtained by Bayesian updating from a diffuse prior distribution, then the equilibrium strategies are log-linear with coefficients obtained by solving a set of linear equations. A similar construction applies to normal distributions and additive terms in the valuation model. An example illustrates the predictions derived from the model. Received: December 11, 1996; revised version: July 15, 1997     

Informational limitations of ascending combinatorial auctions

We study the inherent limitations of natural widely-used classes of ascending combinatorial auctions. Specifically, we show that ascending combinatorial auctions that do not use both non-linear prices and personalized prices cannot achieve social efficiency with general bidder valuations. We also show that the loss of efficiency can be severe and that only a diminishing fraction of the social welfare may be captured. This justifies the added complexity in the auctions suggested by, e.g., Parkes and Ungar (2000) [29] and Ausubel and Milgrom (2002) [2].     

Unobserved correlation in private-value ascending auctions

In private-value ascending auctions, the winner's willingness to pay is not observed, leading to underidentification of many econometric models. I calculate tight bounds on expected revenue and optimal reserve price for the case of symmetric and affiliated private values.     

On ascending Vickrey auctions for heterogeneous objects

We construct an ascending auction for heterogeneous objects by applying a primal-dual algorithm to a linear program that represents the efficient-allocation problem for this setting. The auction assigns personalized prices to bundles, and asks bidders to report their preferred bundles in each round. A bidder's prices are increased when he belongs to a “minimally undersupplied” set of bidders. This concept generalizes the notion of “overdemanded” sets of objects introduced by Demange, Gale, and Sotomayor for the one-to-one assignment problem. Under a submodularity condition, the auction implements the Vickrey-Clarke-Groves outcome; we show that this type of condition is somewhat necessary to do so. When classifying the ascending-auction literature in terms of their underlying algorithms, our auction fills a gap in that literature. We relate our results to various ascending auctions in the literature.     

Simultaneous ascending auctions with complementarities and known budget constraints

We study simultaneous ascending auctions of two identical objects when bidders are financially constrained and their valuations exhibit complementarities. We assume the budget constraints are known but the values for individual objects are private information, and characterize noncollusive equilibria. Equilibrium behavior is affected by the exposure problem. Bidders with higher budgets are more reluctant to bid, because opponents with lower budgets may end up pursuing a single object, thus preventing the realization of complementarities. Therefore poor bidders may win both objects when they do not have the highest valuation. We gratefully acknowledge comments by Marco Battaglini, Benny Moldovanu and participants at seminars held at Montreal, Yale, Texas A&M, Washington St. Louis and at the Workshop on Mechanism Design with Budget Constraints held at SUNY - Stony Brook. Sandro Brusco acknowledges financial support from the Ministerio de Educacion y Ciencias D.G.E.S., proyecto SEC2001-0445.     

The case for multi-unit single-run descending-price auctions

We show that a multiple-unit descending-price auction in which the clock is not reset after each sale may be faster and yield more stable prices than an efficient alternative, thus providing sellers a rationale for using it in practice.     

Sequencing strategies in large, competitive, ascending price automobile auctions: An experimental examination

This paper reports on a large-scale field experiment testing strategies available to a seller participating in simultaneous competitive sequential ascending price automobile auctions. Every other week, the seller offered approximately 100 vehicles for sale in an auction environment in which several competing sellers offered on the order of 3000 vehicles. The experiment tested various sequences in which the seller could offer the vehicles, such as high values first or low values first. Surprisingly, and contrary to intuition drawn from the theory of single item and single seller auctions, the worst performing sequence from those tested is for the seller to order vehicles from highest to lowest values. The best sequence is to group the vehicles by type and offer the low valued vehicles first and then move to offer the higher valued vehicles.     

First-price auctions with resale: the case of many bidders

We study first-price auctions with resale when there are many bidders and derive existence and characterization results under the assumption that the winner of the initial auction runs a second-price auction with an optimal reserve price. The fact that symmetrization fails when there are more than two bidders has been observed before, but we also provide the direction: weaker bidders are less likely to win than stronger ones. For a special class of distributions and three bidders, we prove that the bid distributions are more symmetric with resale than without. Numerical simulations suggest that the more bidders there are, the more similar the allocation is to the case without resale, and thus, the more asymmetric the bid distributions are between strong and weak bidders. We also show in an example that the revenue advantage of first-price auctions over second-price auctions is positive, but decreasing in the number of bidders.     

How (not) to run auctions: The European 3G telecom auctions

There were enormous differences in the revenues from the European “third generation” (3G, or “UMTS”) mobile-phone license auctions, from 20 Euros per capita in Switzerland to 650 Euros per capita in the UK, though the values of the licenses sold were similar. Poor auction designs in some countries facilitated collusion between firms and failed to attract entrants. The sequencing of the auctions was also crucial. We discuss the auctions in the UK, Netherlands, Germany, Italy, Austria, Switzerland, Belgium, Greece and Denmark.     

Ascending auctions for multiple objects: the case for the Japanese design

Summary. We consider two ascending auctions for multiple objects, namely, an English and a Japanese auction, and derive a perfect Bayesian equilibrium of the Japanese auction by exploiting its strategic equivalence with the survival auction, which consists of a finite sequence of sealed-bid auctions. Thus an equilibrium of a continuous time game is derived by means of backward induction in finitely many steps. We then show that all equilibria of the Japanese auction induce equilibria of the English auction, but that many collusive or signaling equilibria of the English auction do not have a counterpart in the Japanese auction.Received: 2 September 2004, Revised: 20 April 2005, JEL Classification Numbers: C72, D44.Fabrizio Germano: Correspondence toWe are indebted to Philippe Jehiel for useful discussions and to Nicolas Vieille for suggestions in the proof of Proposition 2; we also thank seminar audiences in Athens, Basel, Beer-Sheva, Berlin, Brussels, Cambridge, Edinburgh, Exeter, Lausanne, Lisbon, London, Louvain-la-Neuve, Namur and Tel Aviv. Germano acknowledges financial support from Euopean Commission, TMR Network Grant ERBFMRXCT0055, “Cooperation and Information” as well from the Spanish Ministry of Science and Technology, Grants SEC2001-0792, SEJ2004-06319, and in form of a Ramon y Cajal Fellowship. Lovo is member of GREGHEC, unité CNRS, FRE-2810. The support of the Economic and Social Research Council (ESRC) is also gratefully acknowledged. The work was part of the programme of the ESRC Research for Economic Learning and Social Evolution.     

The effectiveness of English auctions

We study the performance of the English auction under different assumptions about the seller's degree of “Bayesian sophistication.” We define the effectiveness of an auction as the ratio between the expected revenue it generates for the seller and the expected valuation of the object to the bidder with the highest valuation (total surplus). We identify tight lower bounds on the effectiveness of the English auction for general private-values environments, and for private-values environments where bidders' valuations are non-negatively correlated. For example, when the seller faces 12 bidders who the seller believes have non-negatively correlated valuations whose expectations are at least as high as 60% of the maximal possible valuation, an English auction with no reserve price generates an expected price that is more than 80% of the value of the object to the bidder with the highest valuation.     

Financial efficiency and economic growth: The case of Spain

This paper explores the connection between financial efficiency and economic growth. First, a theoretical model is presented in which financial efficiency enhances economic growth by means of increasing the marginal productivity of a broad concept of capital. Next, some data from the Spanish economy from 1962 to 1995 are explored using cointegration techniques. The main results point to a prominent role of bank institutions in channeling funds from savings to investment. Operative inefficiency of banks has damaged economic growth by providing a smaller amount of funds to the process of development. These results also suggest the existence of imperfections in Spanish capital markets. Finally, some indicators of financial repression such as negative interest rates and inflation seem to have had a deleterious impact on economic growth.This paper is part of a broader research project financed by Fundación FIES, CECA. Comments by Caneda, Cuñado, Martínez Chacón, Pérez de Villarreal, Termes, and Villaverde are gratefully acknowledged.     

Asymmetric first-price auctions with uniform distributions: analytic solutions to the general case

In 1961, Vickrey posed the problem of finding an analytic solution to a first-price auction with two buyers having valuations uniformly distributed on ${[\underline{v}_{1}, \overline{v}_{1}]}$ and ${[\underline{v}_{2}, \overline{v}_{2}]}$ . To date, only special cases of the problem have been solved. In this paper, we solve this general problem and in addition allow for the possibility of a binding minimum bid. Several interesting examples are presented, including a class where the two bid functions are linear.     

The determinants of efficiency: the case of the Spanish industry

The aim of this paper is to analyse the factors explaining the technical efficiency of Spanish industrial sectors during the period 1991–1994 using the Survey of Business Strategies (SBE) of the Ministry of Industry and Energy. It analyses whether efficiency can be explained by factors external to the firm such as the degree of competition in the markets in which it operates, characteristics of the firm (size, organization, advantages of location, participation of public capital, etc.), as well as the effects of dynamic disturbances that may affect the degree of utilization of the productive capacity.     

The efficiency of government promotion of inbound tourism: The case of Australia

This paper examines the effect of tax-funded promotion of inbound tourism on domestic welfare in an open economy setting with increasing returns in the tourism industry. As inbound tourism is a way of extending the market and getting more demand to realize the implication of increasing returns, promotion can help overcome the underproduction of tourism goods. However, taxation leads to a decline in domestic residents' consumption of tourism and non-tourism goods and reduces the competitiveness of the non-tourism industry in the host country. An important result obtained is that government promotion of inbound tourism will not improve welfare unless the degree of increasing returns in the tourism industry is high enough and the national income of the foreign country multiplied by the parameter of marketing effectiveness is larger than the national income of the home country. This finding is supported by a simulation with the case of Australia.     

The efficiency costs of the postal monopoly: The case of third-class mail

This paper provides an estimate of the efficiency costs of the letter monopoly for third-class bulk advertising, the Postal Service's second largest category of mail. Using market data from private mail carriers, excess costs to mailers in 1992 are estimated to be about $2.5 billion, almost one-third of the Postal Service's third-class mail revenues. These costs are the sum of (1) the allocative efficiency loss due to reduced output ($237 million); (2) the increased production costs due to non-cost-minimizing behavior ($712 million); and (3) transfers to postal labor ($1.511 billion). Total efficiency costs-the sum of (1) and (2)—are estimated to be about $950 million.The author would like to thank Roger Sherman and an anonymous referee for helpful comments and Monica Bettendorf and Stephen McGonegal for their assistance in preparing this paper.     

Organizational efficiency and monopoly power: The case of French industrial groups

In this paper, we examine the respective roles of efficiency and of market power considerations in explaining why industrial groups are the predominant form of organization in specific industries. Our econometric analysis of French industrial groups suggests that administrative and organizational efficiency is an adequate explanation for the existence of these groups and that rivalry between groups differently integrated and diversified is more likely to be the case than collusion.     

Multi-unit demand auctions with synergies: behavior in sealed-bid versus ascending-bid uniform-price auctions

We construct a relatively simple model of bidding with synergies and solve it for both open outcry and sealed-bid uniform-price auctions. The essential behavioral forces involved in these auctions are: (1) A demand reduction force resulting from the monopsony power that bidders with multiple-unit demands have when synergies are relatively inconsequential, and (2) Bidding above stand-alone values in order to capture significant complementarities between units. The latter creates a potential “exposure problem,” as bidders may win only parts of a package and earn negative profits. Bidding outcomes are closer to equilibrium in clock compared to sealed-bid auctions. However, there are substantial and systematic deviations from equilibrium, with patterns of out-of-equilibrium play differing systematically between the two auction formats. These patterns of out-of-equilibrium play are analyzed, along with their effects on revenue and efficiency.