Standard Auction Research Articles

Competitive procurement with ex post moral hazard

AbstractUnlike standard auctions, we show that competitive procurement may optimally limit competition or use inefficient allocation rules that award the project to a less efficient firm with positive probability. Procurement projects often involve ex post moral hazard after the competitive process is over. A procurement mechanism must combine an incentive scheme with the auction to guard against firms bidding low to win the contract and then cutting back on effort. While competition helps reduce the rent of efficient firms, it exacerbates the problem due to moral hazard. If allocative efficiency is a requirement, limiting the number of participants may be optimal. Alternatively, the same incentives can be optimally provided using inefficient allocation rules.

The optimal sequence of prices and auctions

To sell a good before a deadline, a monopolist chooses between posting a price and running a costly reserve-price auction each period. Buyers with independent private values arrive over time. For a wide range of auction costs, the profit-maximizing mechanism sequence is to post prices first and then to run auctions. The optimality of the prices-then-auctions mechanism sequence provides a new justification for the hybrid sales mechanism of allowing the “Buy It Now” option before a standard auction on eBay.

The principles of auction theory (Nobel Memorial Prize in Economic Sciences 2020)

Auction theory is the core of modern economic theory, and standard auctions are the basic elements of many models in microeconomics, public economics, and finance. Theoretical studies of auctions have shaped the modern understanding of the economic role of information in competitive market, and of price theory. Applied analysis of auctions has underpinned important practical mechanisms — for example, mechanisms of privatization and re-privatization of electromagnetic spectrum and public procurement. The 2020 Nobel Memorial Prize in Economic Sciences was awarded to Robert Wilson and Paul Milgrom both for their contributions to the foundations of auction theory and for the development of largescale practical applications.

Competitive Procurement with Ex Post Moral Hazard

Unlike standard auctions, we show that competitive procurement may optimally limit competition or use inefficient allocation rules that award the project to a less efficient firm with positive probability. Procurement projects often involve ex post moral hazard after the competitive process is over. A procurement mechanism must combine an incentive scheme with the auction to guard against firms bidding low to win the contract and then cutting back on effort. While competition helps reduce the rent of efficient firms, it exacerbates the problem due to moral hazard. If allocative efficiency is a requirement, limiting the number of participants may be optimal. Alternatively, the same incentives can be optimally provided using inefficient allocation rules.

Countering the Winner’s Curse: Optimal Auction Design in a Common Value Model

We characterize revenue maximizing mechanisms in a common value environment where the value of the object is equal to the highest of bidders’ independent signals. The optimal mechanism exhibits either neutral selection, wherein the object is randomly allocated at a price that all bidders are willing to pay, or advantageous selection, wherein the object is allocated with higher probability to bidders with lower signals. If neutral selection is optimal, then the object is sold with probability one by a deterministic posted price. If advantageous selection is optimal, the object is sold with probability less than one at a random price. By contrast, standard auctions that allocate to the bidder with the highest signal (e.g., the first-price, second-price or English auctions) deliver lower revenue because of the adverse selection generated by the allocation rule: if a bidder wins the good, then he revises his expectation of its value downward. We further show that the posted price mechanism is optimal among those mechanisms that always allocate the good. A sufficient condition for the posted price to be optimal among all mechanisms is that there is at least one potential bidder who is omitted from the auction. Our qualitative results extend to more general common value environments where adverse selection is high.

Channel Auctions

Standard auction formats feature either an upper bound on the equilibrium price that descends over time (as in the Dutch auction) or a lower bound on the equilibrium price that ascends over time (as in the English auction). We show that in some settings with costly information acquisition, auctions featuring both (viz., a narrowing channel of prices) outperform the standard formats. This Channel auction preserves some of benefits of both the English (truthful revelation) and Dutch (security for necessary information acquisition) auctions. Natural applications include housing, online auction sites like eBay, recording transactions on blockchains, and spectrum rights. This paper was accepted by Joshua Gans, business strategy.

Supplier Diversity Before the Time of Cholera

The current COVID-19 pandemic has highlighted the need to rely on a diverse poolof suppliers, besides achieving cost effectiveness. We propose complementing a shareauction for dual sourcing with affirmative action to create an endogenous set-asidefor a high-cost supplier. In our model more intensive affirmative action strengthensthe targeted provider. This has the potential to level the playing field, inducing morecompetitive procurement overall. Our main result provides a condition under whichthe endogenous set-aside not only guarantees a very substantial share for the high-costsupplier, but also reduces the buyer's provision cost compared to a standard auction.We also illustrate how our approach can help reducing the severity and likelihood ofhealth product shortages, such as those occurred during the recent COVID-19 outbreak.

Premium auctions in the field

In a field experiment, we study the revenue-generating properties of premium auctions. In a premium auction, the runner-up obtains a premium for driving up the price paid by the winner. Previous research, both theoretical and in the lab, has shown that the relative performance of premium auctions compared to standard auction formats is context-specific. In the experiment, we compare two types of premium auctions with the standard Vickrey auction selling high-quality, limited-edition posters in an online auction. We observe that neither premium auction raises higher revenue than the Vickrey auction. Revenue dispersion in the Amsterdam auction, one of the premium auctions, is lower than that in the other two auctions.

Disclosure Policies in All-pay Auctions with Endogenous Entry

This paper examines the effects of disclosing the actual number of bidders in contests with endogenous stochastic entry. I study a standard all-pay auction in which bidders' valuations are commonly known but their participation decisions private. Each potential bidder has to incur an entry cost in order to participate in the auction. It is found that fully concealing the information about the number of participating bidders elicits a higher expected revenue than fully revealing the information if and only if the bidders differ too much in the net gain from winning. In addition, the revenue ranking on disclosure policies varies across the settings with one-sided exogenous entry, one-sided entry cost, and one-sided endogenous entry.

The “Italian Football Federation Auction” for Co-ownership Resolution

The paper is inspired by the Italian Football Federation (FIGC) Auction. The auction was used by the FIGC from the 1950s until 2015 to resolve a 50% co-ownership between two teams in the same league with respect to the performance rights of a football player. Though FIGC banned such joint ownership in 2015, the resolution process is nevertheless interesting with respect to the received literature. In the FIGC Auction each co-owner submits a price offer for the whole asset. The highest bid wins the auction and obtains the asset, while the loser receives as payment the bid that is offered by the winner. Therefore, whether a bidder is a buyer, or a seller, can be established only after the auction has taken place—rather than before the auction. The main contribution of this paper is to investigate the set of pure strategy Nash Equilibria for two extensions of the FIGC Auction, with complete information. The first extension is the Extended Italian Football Federation Auction (EA), where asset shares can differ from 50%. The other extension is the Second Price Extended Italian Football Federation Auction (SEA), which is based on second price rather than first price. As compared to more standard auctions, though in the EA equilibria no bidder may have negative profits, in some circumstances we find that losing the auction may be more profitable than winning the auction. Finally, in the SEA we show that truthful bidding is not a weakly dominant strategy and that—somewhat surprisingly—the set of Nash Equilibria coincides with that of EA.

Optimal Auctions with Signaling Bidders

The authors study optimal auctions in a symmetric private values setting, where bidders’ care about winning the object and a receiver’s inference about their type. They reestablish revenue equivalence when bidders’ signaling concerns are linear, and the auction makes participation observable via an entry fee. With convex signaling concerns, optimal auctions are fully transparent: every standard auction, which reveals all bids yields maximal revenue. With concave signaling concerns there is no general revenue ranking. The authors highlight a trade-off between maximizing revenue derived from signaling, and extracting information from bidders. Their methodology combines tools from mechanism design with tools from Bayesian persuasion.

Countering the winner's curse: Optimal auction design in a common value model

We characterize revenue maximizing mechanisms in a common value environment where the value of the object is equal to the highest of the bidders' independent signals. If the revenue maximizing solution is to sell the object with probability 1, then an optimal mechanism is simply a posted price, namely, the highest price such that every type of every bidder is willing to buy the object. If the object is optimally sold with probability less than 1, then optimal mechanisms skew the allocation toward bidders with lower signals. The resulting allocation induces a “winner's blessing,” whereby the expected value conditional on winning is higher than the unconditional expectation. By contrast, standard auctions that allocate to the bidder with the highest signal (e.g., the first‐price, second‐price, or English auctions) deliver lower revenue because of the winner's curse generated by the allocation. Our qualitative results extend to more general common value environments with a strong winner's curse.

Trust in Procurement Interactions

When complex procurement projects are conducted, it is often not possible to write complete contracts. As a consequence, the relationship between buyer and supplier is important for the success of the project. In this paper we investigate the claim that auctions in procurement can be detrimental for the buyer–supplier relationship, which is in line with the observation that reverse auctions are less frequently conducted if projects are complex. A poor relationship can result in a decrease in trust on the part of the buyer during the sourcing process and an increase in the supplier’s opportunistic behavior following sourcing. We consider a setting in which the winning supplier decides on the level of quality to provide to the buyer, and we compare a standard reverse auction and a buyer-determined reverse auction, both analytically and in the laboratory. We find that the buyer-determined reverse auction can perform better than the standard reverse auction from both the buyer’s and the suppliers’ perspective. In a buyer-determined reverse auction, it may be optimal for the buyer to select the supplier who submitted a higher bid, which may in turn induce this supplier to deliver higher quality. Standard auctions, however, yield lower prices but reduce cooperation. The degree of trust, as reflected by a larger number of transactions and a higher average efficiency of trade, is significantly higher in buyer-determined reverse auctions. Theoretical reasoning based on other-regarding preferences organizes our data well. This paper was accepted by Serguei Netessine, operations management.

Assignment of heterogeneous agents in trees under the permission value

We investigate assignment of heterogeneous agents in trees where the payoff is given by the permission value. We focus on optimal hierarchies, namely those, for which the payoff of the top agent is maximized. For additive games, such hierarchies are always cogent, namely, more productive agents occupy higher positions. The result can be extended to non-additive games with appropriate restrictions on the value function. Next, we consider auctions where agents bid for positions in a vertical hierarchy of depth 2 . Under standard auctions, usually this results in a non-cogent hierarchy.

Collusion-proof and fair auctions

In the standard auction model, we provide a necessary and sufficient condition on the value domain under which non-trivial mechanisms exist that satisfy group strategy-proofness and symmetry. In particular, this condition is satisfied (violated) if values are drawn from a finite set (an interval).

Private and common value auctions with ambiguity over correlation

We analyze auctions when individuals have ambiguity over the joint information structures generating the valuations and signals of players. We analyze how two standard auction effects interact with the ambiguity of bidders over correlation structures. First, a “competition effect” arises when different beliefs about the correlation between bidders' valuations imply different likelihoods of facing competitive bids. Second, a “winner's value effect” arises when different beliefs imply different inferences about the winner's value. In the private values case, only the first effect exists and this implies that the distribution of bids first order stochastically dominates the distribution of bids in the absence of ambiguity. In common value auctions both effects exist and we show that compared to the canonical model, both in the first-price and second-price auctions, these effects combine to imply that the seller's revenue decreases with ambiguity (in contrast with the private values case). We then characterise the optimal auction in both the private and common value cases. A novel feature that arises in the optimal mechanism in the common values case is that the seller only partially insures the high type against ambiguity.

Efficient mechanisms with information acquisition

This paper studies the design of ex ante efficient mechanisms in environments where a single object is for sale, and agents have positively interdependent values and can covertly acquire information at some cost before participating in a mechanism. We find that ex ante efficient mechanisms discourage agents from acquiring excessive information by pooling or randomization. The optimal pooling regions are those where the semi-elasticity of information acquisition is large. There exists an ex ante efficient mechanism that can be implemented by standard auctions with restrictions on the set of allowable bids. In special cases, this implementation is simple and appealing: standard auctions with discrete bids.

Revenue Guarantee Equivalence

We revisit the revenue comparison of standard auction formats, including first-price, second-price, and English auctions. We rank auctions according to their revenue guarantees, i.e., the greatest lower bound of revenue across all informational environments, where we hold fixed the distribution of bidders’ values. We conclude that if we restrict attention to the symmetric affiliated models of Milgrom and Weber (1982) and monotonic pure-strategy equilibria, first-price, second-price, and English auctions are revenue guarantee equivalent: they have the same revenue guarantee, which is equal to that of the first-price auction as characterized by Bergemann, Brooks, and Morris (2017). If we consider all equilibria or if we allow more general models of information, then first-price auctions have a greater revenue guarantee than all other auctions considered. (JEL D44, D83)

Dual sourcing with price discovery

We consider a (standard) reverse auction for dual sourcing and propose to determine both the providers' shares and the reserve price endogenously, depending on the suppliers' bids. Our benchmark considers a two-stage game of complete information. After a first round of bidding, the two most competitive suppliers advance to the second stage and compete again with a refined reserve price, which is based on the lowest price of the excluded providers. We show that at the first stage providers reveal their costs truthfully. At the second stage suppliers balance a trade-off between increasing their share and raising their mark up. Surprisingly, when discarded suppliers are competitive enough, the procedure not only allows taking advantage of dual sourcing but also generates lower procurement expenditures than a standard auction for sole sourcing. We also consider extensions of the benchmark model, including to situations in which providers have private information about their costs.

Auctions with Limited Commitment

We study the role of limited commitment in a standard auction environment. In each period, the seller can commit to an auction with a reserve price but not to future reserve prices. We characterize the set of equilibrium profits attainable for the seller as the period length vanishes. An immediate sale by efficient auction is optimal when there are at least three buyers. For many natural distributions two buyers is enough. Otherwise, we give conditions under which the maximal profit is attained through continuously declining reserve prices. (JEL D44, D82)