First-price Auction Research Articles

Auctioning Long-Term Projects under Financial Constraints

Abstract We consider a procurement auction for the provision of a basic service to which an add-on must later be appended. Potential providers are symmetric, have private information on their cost for the basic service and the winning firm must also implement the add-on. To finance value-enhancing activities related to the add-on, this firm may need extra funding by outside financiers. Non-verifiable effort related to these activities creates a moral hazard problem which makes the firm’s payoff function for the second period concave in returns over the relevant range. Concavity has two effects. First, it makes it more attractive to backload payments to facilitate information revelation. Second, uncertainty on the cost of the add-on introduces a background risk which requires a risk premium. In this context, we characterize the optimal intertemporal structure of payments to the winning firm, equilibrium bidding behavior and reserve prices for a first-price auction.

Optimal procurement auctions with audit

AbstractOne solution to limit the contractor’s default risk in first-price procurement auctions is to audit the winning firm in order to assess the reliability of its bid, and, in case of an unsatisfactory response, move to the firm that ranked second, and so on. Focussing on a situation in which firms with cheaper technologies have a higher risk of default ex-post, we provide conditions that ensure that a first-price auction with audit is indeed optimal. These conditions are likely to be satisfied when the relation between firms’ cost and default risk is not too steep and when the cost of performing the audit is not too large. We also characterize the optimal threshold that determines which firms are to be audited and which are not. We finally discuss cases in which, instead, a first-price auction with audit is dominated by a mechanism in which the allocation (and the audit) is done randomly, at least at some point of the awarding process.

Optimal No-Regret Learning in Repeated First-Price Auctions

In “Optimal No-Regret Learning in Repeated First-Price Auctions,” Y. Han, W. Tsachy, and Z. Zhou study online learning in repeated first-price auctions where a bidder, only observing the winning bid at the end of each auction, learns to adaptively bid to maximize her cumulative payoff. To achieve this goal, the bidder faces censored feedback: If she wins the bid, then she is not able to observe the highest bid of the other bidders, which we assume is i.i.d. drawn from an unknown distribution. In this paper, they develop the first learning algorithm that achieves a near-optimal regret bound, by exploiting two structural properties of first-price auctions, that is, the specific feedback structure and payoff function.

Asymmetric auctions: Perturbations, ε- equilibrium, and equilibrium

We consider first-price auctions with independent and private valuations that have asymmetric valuation distributions and supports. We first show the existence of equilibrium in these auctions through a perturbation approach, thereby establishing that the limit of Bayesian Nash equilibria (BNE) of such perturbed auctions is indeed the Bayesian Nash equilibrium (BNE) of the limit auction with asymmetric supports. We then characterize this BNE and show that the ε-equilibrium (ε-BNE) of the auction with asymmetric supports is a BNE of “close” auctions with common supports. We then demonstrate some numerical examples.

Simultaneous Optimization of Bid Shading and Internal Auction for Demand-Side Platforms

Online advertising has been one of the most important sources for industry's growth, where the demand-side platforms (DSP) play an important role via bidding to the ad exchanges on behalf of their advertiser clients. Since more and more ad exchanges have shifted from second to first price auctions, it is challenging for DSPs to adjust bidding strategy in the volatile environment. Recent studies on bid shading in first-price auctions may have limited performance due to relatively strong hypotheses about winning probability distribution. Moreover, these studies do not consider the incentive of advertiser clients, which can be crucial for a reliable advertising platform. In this work, we consider both the optimization of bid shading technique and the design of internal auction which is ex-post incentive compatible (IC) for the management of a DSP. Firstly, we prove that the joint design of bid shading and ex-post IC auction can be reduced to choosing one monotone bid function for each advertiser without loss of optimality. Then we propose a parameterized neural network to implement the monotone bid functions. With well-designed surrogate loss, the objective can be optimized in an end-to-end manner. Finally, our experimental results demonstrate the effectiveness and superiority of our algorithm.

Participation constraints in first-price auctions

Participation constraints in first-price auctions

Nonparametric Identification and Inference of First-Price Auctions with Heterogeneous Bidders

In the auction literature, it is well established that bidders’ asymmetry plays an important role in determining auction revenues. In this article, we propose a nonparametric methodology to analyze first-price auctions with two popularly adopted asymmetries: heterogeneous risk preferences and asymmetric value distributions. We find that the two competing models provide distinct implications for the bid distributions conditional on heterogeneity. By modeling bidders’ asymmetry as unobserved heterogeneity, we show that the conditional bid distributions are identified nonparametrically. These results enable researchers to test the two competing models. In an application using the US Forest Service timber auction data, we find that the data supports the model with heterogeneity in risk preference.

A Survey on Bid Optimization in Real-Time Bidding Display Advertising

Real-Time Bidding (RTB) is one of the most important forms of online advertising, where an auction is hosted in real time to sell the individual ad impression. How to design an automated bidding strategy in response to the dynamic auction environment is crucial for improving user experience, protecting the interests of advertisers, and promoting the long-term development of the advertising platform. As an exciting topic in the real-world industry, it has attracted great research interest from several disciplines, most notably data science. There have been abundant studies on bidding strategy design which are based on the large volume of historical ad requests. Despite its popularity and significance, few works provide a summary for bid optimization. In this survey, we present the latest overview of the recent works to shed light on the optimization techniques where most of them are validated in practice. We first explore the optimization problem in different works, explaining how these different settings affect the bidding strategy designs. Then, some forms of bidding functions and specific optimization techniques are illustrated. Further, we specifically discuss a new trend about bidding in first-price auctions, which have gradually become popular in recent years. From this survey, both practitioners and researchers can gain insights of the challenges and future prospects of bid optimization in RTB.

Identification of Interdependent Values in Sequential First-Price Auctions

We revisit the (non-)identification of affiliated interdependent-value auctions from the perspective of sequential auctions introduced by Milgrom and Weber (2000). In contrast to static auctions, prices in early rounds affect bidding in later rounds in sequential auctions, generating enough variation for testing interdependent against private values and model identification. We develop nonparametric tests and identification results by exploring the functional dependence of the pseudo values in later rounds on the prices in early rounds. We also discuss applications and extensions of our results, including cases of non-identical goods, observed covariates and unobserved heterogeneity.

Clustered bids in first-price auctions: Collusion or competition?

Clustering of the two most competitive bids in first-price auctions can be indicative of collusive behavior. However, it can also reflect non-cooperative strategies under complete information. I propose a simple procedure to distinguish between the two observationally equivalent explanations. This method requires the knowledge of winning bids and the determinants of the bid of the second most competitive bidder.

Auction design and order of sale with budget-constrained bidders

The presence of financial constraints changes traditional auction theory predictions. In the case of multiple items, such constraints may affect revenue equivalence and efficiency of different auction formats. We consider a simple complete information setting with three financially constrained bidders and two items that have different values common to all the bidders. Using a laboratory experiment, we find that, as predicted by theory, it is more beneficial for the seller to sell the higher value item first. We then show that the first-price sealed-bid auction yields higher revenue than the English auction, with significant differences in learning of equilibrium strategies.

A machine learning-based Biding price optimization algorithm approach

Trading companies of used product market are struggling to gain customers attentaion and to sell the products. The aim of this research is to develop a mechanism that can maximize the sale of products while considering profit implications. The literature review classifies the procurement mechanism. Given the limited-supply nature, that also includes unpredictable quality levels and a procurement mechanism that perceives the company offering prices to suppliers on a single-item basis. The academic literature has not covered such a mechanism. Techniques like those that improve the required bidding strategy are reviewed and considered fit to be included in the support tool as the procedures intention to maximize an objective function depending on the bidding price and contain the probability of winning the auction and the profit made from the proceeding, the motivation laid on the approach that predicts the probability. It is determined that this assembles a Response to Reverse Request for Quotation that meets the assumptions of a First-Price Sealed-Bid(FPSD) auction that potentially includes a hidden reservation price.

Post-auction investment by financially constrained bidders

This study examines auctions in which the value of goods is endogenously determined by ex post investment while bidders face financial constraints. The main results are twofold. First, we characterize performance comparisons on revenue and investment between standard auctions. When the valuation is linear in investment, we have the equivalence theorem with respect to the seller's expected revenue and the winner's expected investment. When the valuation is concave in investment, the first-price auction yields higher expected revenue than the second-price auction. In addition, under additional conditions, the expected investment is larger in the second-price auction. Second, we analyze mechanisms other than simple auctions when sellers aim to promote investment. Scoring auctions increase the winner's investment at the expense of a decrease in revenue compared to price-only auctions.

Application of Game Theory in Different Auction Forms

Auctions are employed in many areas all across the world. It is a key topic of study in game theory. This article primarily summarizes the winning strategies in auctions from a game theory perspective. To examine this issue, this paper reviews the past literature from three auction angles. The winning strategies applied in English auctions, Dutch auctions, and first-price auctions will differ depending on the form of auction. During a customary English auction, the winning strategy is to bid at their genius willingness. However, when multiple goods and deadlines are added to the auction, the winning strategy becomes to bid lower than the valuation. In Dutch auctions, bidders should bid at the beginning at a lower price. In first-price auctions, bidders should bid for all combinations when there are many items, and overbid when there is standard information feedback. This article is a review of previous relevant articles and provides references to related articles.

Spying and imperfect commitment in first-price auctions: a case of tacit collusion

We analyze Stackelberg leadership in a first-price auction. Leadership is induced by an information system, represented by a spy, that leaks one bidder’s bid before others choose their bids. However, the leader may secretly revise his bid with some probability; therefore, the leaked bid is only an imperfect signal. Whereas leadership with perfect commitment exclusively benefits the follower, imperfect commitment yields a collusive outcome, even if the likelihood that the leader may revise his bid is arbitrarily small. This collusive impact shows up in all equilibria and is strongest in the unique pooling equilibrium which is also payoff dominant.

Robust Bidding in First-Price Auctions: How to Bid Without Knowing What Others Are Doing

We propose how to bid in first-price auctions when a bidder knows the own value but not how others will bid. To do this, we introduce a methodology to show how to make choices in strategic settings without assuming common knowledge or equilibrium behavior. Accordingly, we first eliminate environments that are believed not to occur and then find a robust rule that performs well in the remaining environments. We test our bids using data from laboratory experiments and the field and find that our bids outperform those made by real bidders. This paper was accepted by Omar Besbes, revenue management and market analytics. Supplemental Material: The online appendix and data are available at https://doi.org/10.1287/mnsc.2023.4899 .

Speculation in procurement auctions

A speculator can take advantage of a procurement auction by acquiring items for sale before the auction. The accumulated market power can then be exercised in the auction and may lead to a large enough gain to cover the acquisition costs. I show that speculation always generates a positive expected profit in second-price auctions but could be unprofitable in first-price auctions. In the case where speculation is profitable in first-price auctions, it is more profitable in second-price auctions. This comparison in profitability is driven by different competition patterns in the two auction mechanisms: in first-price auctions, sellers who refuse to sell to the speculator bid more aggressively than in second-price auctions. In terms of welfare, speculation causes private value destruction and harms efficiency. Sellers benefit from the acquisition offer made by the speculator. Therefore, speculation comes at the expense of the auctioneer.

A Trustable and Secure Usage-Based Insurance Policy Auction Mechanism and Platform Using Blockchain and Smart Contract Technologies.

This study presents an architectural framework for the blockchain-based usage-based insurance (UBI) policy auction mechanism in the internet of vehicles (IoV) applications. The main objective of this study is to analyze and design the specific blockchain architecture and management considerations for the UBI environment. An auction mechanism is developed for the UBI blockchain platform to enhance consumer trust. The study identifies correlations between driving behaviors and associated risks to determine a driver's score. A decentralized bidding algorithm is proposed and implemented on a blockchain platform using elliptic curve cryptography and first-price sealed-bid auctions. Additionally, the model incorporates intelligent contract functionality to prevent unauthorized modifications and ensure that insurance prices align with the prevailing market value. An experimental study evaluates the system's efficacy by expanding the participant pool in the bidding process to identify the winning bidder and is investigated under scenarios where varying numbers of insurance companies submit bids. The experimental results demonstrate that as the number of insurance companies increases exponentially, the temporal overhead incurred by the system exhibits only marginal growth. Moreover, the allocation of bids is accomplished within a significantly abbreviated timeframe. These findings provide evidence that supports the efficiency of the proposed algorithm.

Estimating damages from bidding rings in first-price auctions

Bidding rings typically coordinate to rig auctions and keep prices low. Despite bid rigging being pervasive, measuring its damages (i.e., the revenue loss suffered by the auctioneer) is a challenge for antitrust authorities. Indeed, most of the methods to quantify damages compare outcomes of auctions affected by the collusive behavior with unaffected auctions, requiring data that is hard to obtain. We propose a model-based method to estimate damages. Its main advantages are that only information on affected auctions is required and that the underlying assumptions of the economic model are explicit, so they can be challenged and eventually modified for damage reassessment. In a Monte Carlo exercise, we show that our methodology performs well in moderate-size samples. We apply our method to data from the Ohio milk cartel and estimate damages similar to those found in previous studies, even when we discard information from non-affected markets.

Optimal Procurement with Quality Concerns

Adverse selection in procurement arises when low-cost bidders are also low-quality suppliers. We propose a mechanism called LoLA (lowball lottery auction) which, under some conditions, maximizes any combination of buyer’s and social surplus, subject to incentive compatibility, in the presence of adverse selection. The LoLA features a floor price, and a reserve price. The LoLA has a dominant strategy equilibrium that, under mild conditions, is unique. In a counterfactual analysis of Italian government auctions, we compute the gain that the government could have made, had it used the optimal procurement mechanism (a LoLA), relative to a first-price auction (the adopted format). (JEL D44, D82, H57, L14)