Auctions with Price-Proportional Benefits to Bidders

After some auctions, including Amish estate sales and buyer rings′ knockout auctions, each bidder receives a share of the revenue generated by the auction. We show that in the symmetric case, equilibrium bids in both first-price sealed-bid auctions and oral auctions increase as each bidder′s share increases. In the case of independent signals, oral auctions result in higher expected equilibrium prices than do first-price sealed-bid auctions. Journal of Economic, Literature classification number: D44.     

Strategic Jump Bidding in English Auctions

This paper solves for equilibria of sequential bid (or English) auctions with affiliated values when jump bidding strategies may be employed to intimidate one's opponents. In these equilibria, jump bids serve as correlating devices which select asymmetric bidding functions to be played subsequently. Each possibility of jump bidding provides a Pareto improvement for the bidders from the symmetric equilibrium of a sealed bid, second-price auction. The expanded set of equilibria can approximate either first- or second-price outcomes and produce exactly the set of expected prices between those two bounds. These results contrast with standard conclusions that equate English and second-price auctions.     

Reserve price signaling

In a general auction model in which bidders’ signals are affiliated, we characterize the unique separating equilibrium in which the seller can use reserve prices to credibly signal her private information. When the buyers’ signals are independent, the optimal reserve price is shown to be increasing in the number of bidders under certain conditions. We also demonstrate that the probability that the item is sold at the reserve price can increase as the number of bidders increases, which indicates a more central role for reserve prices than perceived in the standard auction models.     

Expected revenue of all-pay and first-price sealed-bid auctions with affiliated signals

In the general symmetric auction framework of Milgrom and Weber (1982) it is shown—as a new manifestation of thelinkage principle—that the all-pay sealed-bid auction yieldshigher expected revenue than the standard first-price sealed-bid auction. This raises the question why sealed-bid auctions of the standard first-price variety are observed in practice whereas the all-pay variety is not.     

Sequential versus Bundle Auctions for Recurring Procurement

We compare sequential and bundle procurement auctions in a framework of successive procurement situations, where current success positively or negatively affects future market opportunities. We find that in bundle auctions procurement cost is lower and less risky than in sequential standard auctions, but still higher than in the optimal sequential auction. Only a sequential second price auction leads to the efficient outcome.     

Unique Implementation of the Full Surplus Extraction Outcome in Auctions with Correlated Types

In auctions with correlated types it is possible to design mechanisms such that full surplus extraction can be obtained as the outcome of an equilibrium in which agents use (weakly) dominant strategies. However, it is not assured that the outcome is unique. We present an example in which no mechanism can yield the full surplus extraction outcome as the unique Bayesian equilibrium outcome. Next we show that in the standard auction model the multiplicity problem can be fully resolved using sequential mechanisms, i.e., we show that it is possible to obtain the full surplus extraction outcome as the unique perfect Bayesian equilibrium outcome.Journal of Economic LiteratureClassification Numbers: D44; D70.     

Competitive auctions

We study a class of single-round, sealed-bid auctions for an item in unlimited supply, such as a digital good. We introduce the notion of competitive auctions. A competitive auction is truthful (i.e. encourages bidders to bid their true valuations) and on all inputs yields profit that is within a constant factor of the profit of the optimal single sale price. We justify the use of optimal single price profit as a benchmark for evaluating a competitive auctions profit. We exhibit several randomized competitive auctions and show that there is no symmetric deterministic competitive auction. Our results extend to bounded supply markets, for which we also give competitive auctions.     

Sequentially Optimal Auctions

In auctions where a seller can post a reserve price but if the object fails to sell cannot commit never to attempt to resell it, revenue equivalence between repeated first price and second price auctions without commitment results. When the time between auctions goes to zero, seller expected revenues converge to those of a static auction with no reserve price. With many bidders, the seller equilibrium reserve price approaches the reserve price in an optimal static auction. An auction in which the simple equilibrium reserve price policy of the seller mirrors a policy commonly used by many auctioneers is computed.Journal of Economic LiteratureClassification Numbers: C78, D44, D82.     

An Optimal Auction for Complements

This paper considers the optimal selling mechanism for complementary items. When buyers are perfectly symmetric, the optimal procedure is to bundle the items and run a standard auction. In general, however, bundling the items is not necessarily desirable, and the standard auctions do not maximize revenue. Moreover, the optimal auction allocation may not be socially efficient since the auction must discriminate against bidders who have strong incentives to misrepresent their true preferences.Journal of Economic LiteratureClassification Number: D44.     

Auctions in which losers set the price

We study auctions of a single asset among symmetric bidders with affiliated values. We show that the second-price auction minimizes revenue among all efficient auction mechanisms in which only the winner pays, and the price only depends on the losers' bids. In particular, we show that the kth price auction generates higher revenue than the second-price auction, for all k>2. If rationing is allowed, with shares of the asset rationed among the t highest bidders, then the (t+1)st price auction yields the lowest revenue among all auctions with rationing in which only the winners pay and the unit price only depends on the losers' bids. Finally, we compute bidding functions and revenue of the kth price auction, with and without rationing, for an illustrative example much used in the experimental literature to study first-price, second-price and English auctions.     

First-price equilibrium and revenue equivalence in a sequential procurement auction model

We analyze first-price equilibrium bidding behavior of capacity-constrained firms in a sequence of two procurement auctions. In the model, firms with a cost advantage in completing the project auctioned off at the end of the sequence may enter the unfavored first auction hoping to lose it. Equilibrium bidding in both auctions deviates from the standard Symmetric Independent Private Value auction model due to opportunity costs of bidding created by possibly employed capacity. For this sequential auction model with non-identical objects, we show that revenue equivalence applies.     

Internet auctions with many traders

We study a multi-unit auction environment similar to eBay. Sellers, each with a single unit of a homogeneous good, set reserve prices at their own second-price auctions. Each buyer has private value for the good and wishes to acquire a single unit. Buyers can bid as often as they like and move between auctions. We characterize a perfect Bayesian equilibrium for this decentralized dynamic mechanism in which, conditional on reserve prices, an efficient set of trades occurs at a uniform price. In a large but finite market, the sellers set reserve prices equal to their true costs under a very mild distributional assumption, so ex post efficiency is achieved. Buyers’ strategies in this equilibrium are simple and do not depend on their beliefs about other buyers’ valuations, or the number of buyers and sellers.     

The determinants of price in 3G spectrum auctions

This article examined the empirical relationship between prices paid for national 3G wireless licenses when spectrums were sold by auction. The reduced-form modelling approach was based on the premise that auction design features can, and do, affect both final (revenue) and intermediate (viz., auction competitiveness and license assignment) auction outcomes. Importantly, the analysis recognizes, and explicitly allows for, the endogeneity of bidder entry and sample selection arising from an absence of bidding. Generally, these key features have only received attention in isolation. In particular, the study addressed the principal question of: which regulator chosen auction design variables determine prices paid in spectrum auctions? The analysis showed that flexible-package formats increased prices paid, and that higher reserve prices had a dampening effect. The article also showed that longer license terms and more competitive auctions (as measured by the bidders-to-licenses ratio) enhance prices paid.     

Market behavior in bid,offer, and double auctions: A Reexmination

This study examines the robustness of the previously observed [Smith (1964)] differences in market behavior between double auctions (both buyers and sellers may enter price quotes), bid auctions (only buyers may enter price quotes), and offer auctions (only sellers may enter price quotes). Based on the results of twenty-one market experiments, we find little support for the a priori hypothesis that bid auction prices tend to be greater than double auction prices which tend to be greater than offer auction prices.     

Bidders' and Sellers' Strategies in Sequential Auctions. New Evidence about the Afternoon Effect

Using dynamic panel data econometric techniques, we analyzethe price structure of sequential auctions of modern and contemporary art that took place inItaly during the period 1983–1996. Contrary to previous empirical studies, we do not find anyafternoon effect, or decline of auction prices relative to estimated values. Taking intoconsideration the structure of the auctions and the dynamic nature of price determination, we proposean interpretation of the empirical results that encompasses previous contributions.     

BIDS AND COSTS IN COMBINATORIAL AND NONCOMBINATORIAL PROCUREMENT AUCTIONS—EVIDENCE FROM PROCUREMENT OF PUBLIC CLEANING CONTRACTS

Combinatorial procurement auctions enable suppliers to pass their potential cost synergies on to the procuring entity and may therefore lead to lower costs and enhance efficiency. However, bidders might find it profitable to inflate their stand‐alone bids in order to favor their package bids. Using data from standard and combinatorial procurement auctions, we find that bids on individual contracts in simultaneous standard auctions without the option to submit package bids are significantly lower than the corresponding stand‐alone bids in combinatorial auctions. Further, no significant difference in procurer's cost as explained by auction format is found. (JEL D44, H57, L15)     

Ascending price Vickrey auctions

We show that an ascending price auction for multiple units of a homogeneous object proposed by Ausubel (i) raises prices for packages until they reach those nonlinear and non-anonymous market clearing prices at which bidders get their marginal products and (ii) the auction is a primal–dual algorithm applied to an appropriate linear programming formulation in which the dual solution yields those same market clearing prices. We emphasize the similarities with efficient incentive compatible ascending price auctions to implement Vickrey payments when there is a single object or when objects are heterogeneous but each buyer does not desire more than one unit. A potential benefit of these common threads is that it helps to establish the principles upon which Vickrey payments may be implemented through decentralized, incentive compatible procedures.     

Endogenous Entry and Exit in Common Value Auctions

We develop and experimentally test a model of endogenous entry, exit, and bidding in common value auctions. The model and experimental design include an alternative profitable activity (a safe haven) that provides agentspecific opportunity costs of bidding in the auction. Each agent chooses whether to accept the safe haven income or forgo it in order to bid in the auction. Agents that enter the auction receive independently-drawn private signals that provide unbiased estimates of the common value. The auctioned item is allocated to the high bidder at a price that is equal to the high bid. Thus the market is a first-price sealed-bid common value auction with endogenous determination of market size.     

Auctions with a buy price

eBay and Yahoo allow sellers to list their auctions with a buy price at which a bidder may purchase the item immediately. On eBay, the buy-now option disappears once a bid is placed, while on Yahoo the buy-now option remains in effect throughout the auction. We show that when bidders are risk averse, both types of auctions raise seller revenue for a wide range of buy prices. The Yahoo format raises more revenue than the eBay format when bidders have either CARA or DARA. Bidders with DARA prefer the eBay auction, while bidders with CARA are indifferent between the two. Part of this work was completed while Reynolds was a visitor at Instituto de Analisys Economico in Barcelona and while Wooders was a visitor at Hong Kong University of Science and Technology. We are grateful to these institutions for their hospitality.     

Mixed bundling auctions

We study multi-object auctions where agents have private and additive valuations for heterogeneous objects. We focus on the revenue properties of a class of dominant strategy mechanisms where a weight is assigned to each partition of objects. The weights influence the probability with which partitions are chosen in the mechanism. This class contains efficient auctions, pure bundling auctions, mixed bundling auctions, auctions with reserve prices and auctions with pre-packaged bundles. For any number of objects and bidders, both the pure bundling auction and separate, efficient auctions for the single objects are revenue-inferior to an auction that involves mixed bundling.