Auctions with selective entry and risk averse bidders: theory and evidence

We study auctions with selective entry and risk averse bidders. Our model accounts for risk averse bidders' endogenous participation decision and thus encompasses the existing entry models. We establish entry and bidding equilibrium in first‐price auction and ascending auction mechanisms and show that bidders' entry behavior differs between these two mechanisms with different forms of risk aversion. Our approach provides testable implications of risk aversion in terms of entry behavior. We analyze a timber auction data set and propose a simple test for the form of bidders' risk aversion based on our model implications.     

A Parimutuel Market Microstructure for Contingent Claims

Parimutuel principles are widely used as an alternative to fixed odds gambling in which a bookmaker acts as a dealer by quoting fixed rates of return on specified wagers. A parimutuel game is conducted as a call auction in which odds are allowed to fluctuate during the betting period until the betting period is closed or the auction ‘called’. The prices or odds of wagers are set based upon the relative amounts wagered on each risky outcome. In financial microstructure terms, trading under parimutuel principles is characterised by (1) call auction, non‐continuous trading; (2) riskless funding of claim payouts using the amounts paid for all of the claims during the auction; (3) special equilibrium pricing conditions requiring the relative prices of contingent claims equal the relative aggregate amounts wagered on such claims; (4) endogenous determination of unique state prices; and (5) higher efficiency. Recently, a number of large investment banks have adopted a parimutuel mechanism for offering contingent claims on various economic indices, such as the US Nonfarm payroll report and Eurozone Harmonised inflation. Our paper shows how the market microstructure incorporating parimutuel principles for contingent claims which allows for notional transactions, limit orders, and bundling of claims across states is constructed. We prove the existence of a unique price equilibrium for such a market and suggest an algorithm for computing the equilibrium. We also suggest that for a broad class of contingent claims, that the parimutuel microstructure recently deployed offers many advantages over the dominant dealer and exchange continuous time mechanisms.     

Information feedback in first price auctions

I apply the notion of a self‐confirming equilibrium (SCE) to study how feedback in first price auctions influences bidders' perceptions about their strategic environment, and consequently their bidding behavior. In a private values setting, revealing the two highest bids at the end of each auction is sufficient for bidders to have correct beliefs (justifying the assumption of Nash equilibrium). In contrast, in every symmetric SCE of a symmetric, affiliated, private values model, bidding strategies and revenue are (weakly) higher if only the highest bid is revealed. I also consider interdependent valuations and discuss implications for the empirical auction literature.     

First‐price auctions with resale and with outcomes robust to bid disclosure

Although there exists a pure separating equilibrium of the two‐bidder first‐price auction with resale when the bids are kept secret, the ratchet effect prevents the existence of such an equilibrium if the bidders are heterogeneous and the bids are fully disclosed. Nevertheless, we construct a behavioral equilibrium under full disclosure that is equivalent to the pure separating equilibrium under no disclosure. Thus, if the bidders follow this equilibrium, the choice of the disclosure regime does not affect the final allocation of the item nor the expected payoffs.     

Buy or wait,that is the option: the buyer's option in sequential laboratory auctions

We report results from an experiment on two‐unit sequential auctions with and without a buyer's option (which allows the winner of the first auction to buy the second unit). The four main auction institutions are studied. Observed bidding behavior is close to Nash equilibrium bidding in the auctions for the second unit, but not in the auctions for the first unit. Despite these deviations, the buyer's option is correctly used in most cases. The revenue ranking of the four auctions is the same as in single‐unit experiments. Successive prices are declining when the buyer's option is available.     

Regulating bidder participation in auctions

Regulating bidder participation in auctions can potentially increase efficiency compared to standard auction formats with free entry. We show that the relative performance of two such mechanisms, a standard first‐price auction with free entry and an entry rights auction, depends nonmonotonically on the precision of information that bidders have about their costs prior to deciding whether to participate in a mechanism. As an empirical application, we estimate parameters from first‐price auctions with free entry for bridge‐building contracts in Oklahoma and Texas and predict that an entry rights auction increases efficiency and reduces procurement costs significantly.     

Resource Allocation Auctions within Firms

There is growing interest in the use of markets within firms. Proponents have noted that markets are a simple and efficient mechanism for allocating resources in economies in which information is dispersed. In contrast to the use of markets in the broader economy, the efficiency of an internal market is determined in large part by the endogenous contractual incentives provided to the participating, privately informed agents. In this paper, we study the optimal design of managerial incentives when resources are allocated by an internal auction market, as well as the efficiency of the resulting resource allocations. We show that the internal auction market can achieve first‐best resource allocations and decisions, but only at an excessive cost in compensation payments. We then identify conditions under which the internal auction market and associated optimal incentive contracts achieve the benchmark second‐best outcome as determined using a direct revelation mechanism. The advantage of the auction is that it is easier to implement than the direct revelation mechanism. When the internal auction mechanism is unable to achieve second‐best, we characterize the factors that determine the magnitude of the shortfall. Overall, our results speak to the robust performance of relatively simple market mechanisms and associated incentive systems in resolving resource allocation problems within firms.     

Bidding into the Red: A Model of Post-Auction Bankruptcy

This paper investigates auctions where bidders have limited liability. First, we analyze bidding behavior under different auction formats, showing that the second‐price auction induces higher prices, higher bankruptcy rates, and lower utilities than the first‐price auction. Second, we show that the cost of bankruptcy critically affects the seller's preference over the choice of auction. If bankruptcy is very costly, the seller prefers the first‐price auction over the second‐price auction. Alternatively, if the bankrupt assets are resold among the losers of the initial auction, the seller prefers the second‐price auction.     

An empirical study of auction revenue rankings: the case of municipal bonds

Using a novel dataset of 386 first‐price municipal bond auctions held in California, I perform counterfactual revenue comparisons, based on the theoretical result of Milgrom and Weber (1982). I show that the revenue in the second‐price auction is nonparametrically identified, and the counterfactual revenue in the English auction can be bounded in an informative way. These results form a basis for nonparametric estimation of counterfactual revenue differences. I find that the revenue gain from using the English auction would be in the range of 11%—19% of the gross underwriting spread, and that most of it would already be captured by using the second‐price auction. The recent explosive growth of Internet English auctions, administered by Grant Street Group, provides external support to the claim that auction design matters in this market.     

Choice of Selling Mechanism at the IPO: the Case of the French Second Market

This study examines the choice of flotation mechanism within the framework of the French Second Market. Between 1983 and 1996, a firm that opted for a quotation on the Second Market, had the choice between (i) an auction‐like procedure (there were two variants) and (ii) a fixed‐price introduction procedure. Several interesting results are presented. First, the choice for an auction‐like procedure appears to be positively related to firm valuation uncertainty at the IPO. Second, the likelihood of opting for an auction‐like procedure decreases as the reputation of the investment bank guiding the flotation increases. Third, the likelihood of opting for an auction is increasing in the number of secondary shares sold by venture capitalists and investment banks.     

Dynamic auction environment with subcontracting

This article provides evidence on the role of subcontracting in the auction‐based procurement setting with private cost variability and capacity constraints. We demonstrate that subcontracting allows bidders to modify their costs realizations in a given auction as well as to control their future costs by reducing backlog accumulation. Restricting access to subcontracting raises procurement costs for an individual project by 12% and reduces the number of projects completed in equilibrium by 20%. The article explains methodological and market design implications of subcontracting availability.     

Learning by bidding

We analyze a dynamic second‐price auction with an informed bidder and an uninformed bidder who, upon seeing a posted price, learns whether his valuation is above that price. In the essentially unique equilibrium, an informed bidder bids in the first period if her valuation is below some cutoff and bids only in the last period otherwise. An uninformed bidder bids in every period to optimally change the price unless the price is above his valuation or he is the high bidder. This model also provides a rationale behind the use of a secret reserve price in private‐value settings.     

Endogenous asymmetry in a dynamic procurement auction

We show how to numerically solve for a Markov‐perfect equilibrium of a dynamic auction game where a procurer repeatedly purchases construction services from capacity‐constrained firms. We find that the procurer is best off scheduling frequent auctions for small project sizes. Otherwise, firm capacity utilization rates become larger and more asymmetric, which softens competition and increases procurement costs. We also find that forward‐looking bidding dampens the competition‐softening effects of asymmetry: farsighted firms compete more intensely than myopic ones. This can undermine the goal of a bid‐preference‐style affirmative action program: more farsighted firms respond less to the asymmetry induced via bid preferences.     

Best foot forward or best for last in a sequential auction?

Should a seller with private information sell the best or worst goods first? Considering the sequential auction of two stochastically equivalent goods, we find that the seller has an incentive to impress buyers by selling the better good first because the seller's sequencing strategy endogenously generates correlation in the values of the goods across periods. When this impression effect is strong enough, selling the better good first is the unique pure‐strategy equilibrium. By credibly revealing to all buyers the seller's ranking of the goods, an equilibrium strategy of sequencing the goods reduces buyer information rents and increases expected revenues in accordance with the linkage principle.     

Buy‐out prices in auctions: seller competition and multi‐unit demands

Online auction sites often enable sellers to add a buy‐out price. In one‐shot auctions, this has been motivated by appeal to impatience or risk aversion. We offer additional justification in a dynamic model, by showing that an early seller has an incentive to use a buy‐out price, if a similar product is offered later by another seller, and bidders desire multiple objects. Revenue in the first auction increases, but revenue in the second auction decreases, as does the sum of revenues. The buy‐out price causes the auction sequence to become inefficient, because the first item may be awarded to a bidder who should have received none.     

A computational framework for analyzing dynamic auctions: The market impact of information sharing

This article develops a computational framework to analyze dynamic auctions and uses it to investigate the impact of information sharing among bidders. We show that allowing for the dynamics implicit in many auction environments enables the emergence of equilibrium states that can only be reached when firms are responding to dynamic incentives. The impact of information sharing depends on the extent of dynamics and provides support for the claim that information sharing, even of strategically important data, need not be welfare reducing. Our methodological contribution is to show how to adapt the experience-based equilibrium concept to a dynamic auction environment and to provide an implementable boundary-consistency condition that mitigates the extent of multiple equilibria.     

Subcontracting and competitive bidding on incomplete procurement contracts

This article examines the impact of incomplete contracts on subcontracting and the design of procurement auctions. I estimate the effect of ex post contract revisions on unit costs for both subcontracted and in‐house performed work items on bridge projects procured by the California Department of Transportation. I model a scoring auction showing how ex post revisions skew bidding decisions and estimate unit costs from bid data using the method of sieve estimation. The results highlight the cost implications of incomplete contracting frictions, subcontracting decisions, and bidding distortions. In conclusion, I propose alternative auction mechanisms that could improve outcomes.     

Field experiments on the effects of reserve prices in auctions: more Magic on the Internet

I present experimental evidence on the effects of minimum bids in first‐price, sealed‐bid auctions. The auction experiments manipulated the minimum bids in a preexisting market on the Internet for collectible trading cards from the game Magic: the Gathering. I examine a number of outcomes, including the number of participating bidders, the probability of sale, the levels of individual bids, and the auctioneer's revenues. The benchmark theoretical model is one with symmetric, risk‐neutral bidders with independent private values. The results verify a number of the predictions concerning equilibrium bidding. Many bidders behave strategically, anticipating the effects of the reserve price on others' bids.     

Bidding to lose? Auctions with resale

A losing bidder can still purchase the prize from the winner after the auction. We show why a strong bidder may prefer to drop out of the auction before the price has reached her valuation and acquire the prize in the aftermarket: a strong bidder may be in a better bargaining position in the aftermarket if her rival won at a relatively low price. So it can be common knowledge that, in equilibrium, a weak bidder will win the auction and, even without uncertainty about relative valuations, resale will take place. The possibility of reselling to a strong bidder attracts weak bidders to participate in the auction and raises the seller's revenue.     

Price Discovery in the Treasury‐Bill When‐Issued Market

When‐issued (i.e., forward) trading in T‐bills yet to be auctioned provides a unique environment for examining price discovery. Because T‐bills are auctioned in a sealed‐bid process, when‐issued traders cannot observe the spot market price. Yet the forward price must ultimately converge on the auction outcome price. Our results indicate that traders in the when‐issued market “discover” the ultimate auction price. Little evidence is found that standard order flow variables contribute to price discovery. Instead, the ability to observe a few trades with relatively small volume in the when‐issued market is sufficient to discover the auction price resulting from the sealed‐bid process.