First-price Auction Research Articles

Credibility in second-price auctions: an experimental test

We provide the first direct test of how the credibility of an auction format affects bidding behavior and final outcomes. To do so, we conduct a series of laboratory experiments where the role of the seller is played by a human subject who receives the revenue from the auction and who (depending on the treatment) has agency to determine the outcome of the auction. Contrary to theoretical predictions, we find that the non-credible second-price auction fails to converge to the first-price auction. We provide a behavioral explanation for our results based on sellers’ aversion to rule-breaking, which is confirmed by an additional experiment.

Rejection prices and an auctioneer with non-monotonic utility

This paper considers an auctioneer who has a non-monotonic utility function with a unique maximizer. The auctioneer is able to reject all bids over some amount by using rejection prices. We show that the optimal rejection price for such an auctioneer is lower than and equal to that maximizer in first-price and second-price sealed-bid auctions, respectively. Further, in each auction we characterize a necessary and sufficient condition that by using the optimal rejection price not only the auctioneer but also bidders can be better off, compared to a standard auction. Finally, we find that the auctioneer strictly prefers a first-price sealed-bid auction if he is risk-averse when his revenue is lower than the maximizer or if the distribution of revenues which are lower than the maximizer in a standard first-price sealed-bid auction is first-order stochastic dominant over the one in a standard second-price sealed-bid auction.

Design of the contingent royalty rate as related to the type of investment

This study investigates the design of the royalty rate in a first-price auction across three types of investments: incremental and lumpy with or without an exogenously given intensity. A bidder’s investment cost comprises private information. This, together with the stochastic evolution of the price of the output generated from the auctioned project, precludes the seller from setting the exact dates of investment with the winner. However, the seller can set the royalty rate to equate the winner’s royalty payment with the winner’s information rent so that the winner acts as if to maximize the seller’s revenue. We derive two main conclusions. First, compared with the case in which investment is lumpy with an exogenously given intensity, the seller can set a lower royalty rate on incremental investment because she can collect additional royalty payments from the winner, who has the option to later expand capacity. Second, the impact of output price uncertainty on the optimal royalty rate for the three types of investments exhibits two different patterns. When investment is either incremental or lumpy with an exogenously given intensity, greater output price uncertainty reduces the royalty rate. When investment is lumpy with variable intensity, greater output uncertainty raises the royalty rate. Our results imply that auctioneers may charge differential royalty rates for different types of investments.

Distributionally Robust Batch Contextual Bandits

Policy learning using historical observational data are an important problem that has widespread applications. Examples include selecting offers, prices, or advertisements for consumers; choosing bids in contextual first-price auctions; and selecting medication based on patients’ characteristics. However, existing literature rests on the crucial assumption that the future environment where the learned policy will be deployed is the same as the past environment that has generated the data: an assumption that is often false or too coarse an approximation. In this paper, we lift this assumption and aim to learn a distributionally robust policy with incomplete observational data. We first present a policy evaluation procedure that allows us to assess how well the policy does under worst-case environment shift. We then establish a central limit theorem type guarantee for this proposed policy evaluation scheme. Leveraging this evaluation scheme, we further propose a novel learning algorithm that is able to learn a policy that is robust to adversarial perturbations and unknown covariate shifts with a performance guarantee based on the theory of uniform convergence. Finally, we empirically test the effectiveness of our proposed algorithm in synthetic datasets and demonstrate that it provides the robustness that is missing using standard policy learning algorithms. We conclude the paper by providing a comprehensive application of our methods in the context of a real-world voting data set.This paper was accepted by Hamid Nazerzadeh, data science.Funding: This work was supported by the National Science Foundation [Grant CCF-2106508] and the Air Force Office of Scientific Research [Award FA9550-20-1-0397]. Z. Zhou also gratefully acknowledges the JP Morgan AI Research Grant and the New York University’s Center for Global Economy and Business faculty research grant for support on this work. Additional support is gratefully acknowledged from the National Science Foundation [Grants 1915967 and 2118199].Supplemental Material: The data files and online appendix are available at https://doi.org/10.1287/mnsc.2023.4678 .

Delay-Adaptive Learning in Generalized Linear Contextual Bandits

In this paper, we consider online learning in generalized linear contextual bandits where rewards are not immediately observed. Instead, rewards are available to the decision maker only after some delay, which is unknown and stochastic. Such delayed feedback occurs in several active learning settings, including product recommendation, personalized medical treatment selection, bidding in first-price auctions, and bond trading in over-the-counter markets. We study the performance of two well-known algorithms adapted to this delayed setting: one based on upper confidence bounds and the other based on Thompson sampling. We describe modifications on how these two algorithms should be adapted to handle delays and give regret characterizations for both algorithms. To the best of our knowledge, our regret bounds provide the first theoretical characterizations in generalized linear contextual bandits with large delays. Our results contribute to the broad landscape of contextual bandits literature by establishing that both algorithms can be made to be robust to delays, thereby helping clarify and reaffirm the empirical success of these two algorithms, which are widely deployed in modern recommendation engines. Funding: This work was supported by the National Science Foundation [Grants 2118199, 1915967, and CCF-2106508], the Air Force Office of Scientific Research [Award FA9550-20-1-0397], a Digital Twin research grant from Bain & Company, and a faculty research grant from New York University’s Center for Global Economy and Business.

Edge-side task scheduling: Auction mechanism and genetic algorithm based methods

Edge computing is an emerging computing architecture. The scheduling and optimization of the tasks on the edge side of the smart factory can effectively reduce the processing delay and improve the utilization efficiency of servers. This study focuses on the problem of edge-side task scheduling with the goal of minimizing the maximum completion time of the tasks. A first-price sealed-bid auction based algorithm and a genetic algorithm with elite retention strategy are designed to solve the problem. The experimental results indicate that the auction-based scheduling algorithm has better real-time performances compared to the genetic algorithm.

Cross-game learning and cognitive ability in auctions

Overbidding in sealed-bid second-price auctions (SPAs) has been shown to be persistent and associated with cognitive ability. We study experimentally to what extent cross-game learning can reduce overbidding in SPAs, taking into account cognitive skills. Employing an order-balanced design, we use first-price auctions (FPAs) to expose participants to an auction format in which losses from high bids are more salient than in SPAs. Experience in FPAs causes substantial cross-game learning for cognitively less able participants but does not affect overbidding for the cognitively more able. Vice versa, experiencing SPAs before bidding in an FPA does not substantially affect bidding behavior by the cognitively less able but, somewhat surprisingly, reduces bid shading by cognitively more able participants, resulting in lower profits in FPAs. Thus, ‘cross-game learning’ may rather be understood as ‘cross-game transfer’, as it has the potential to benefit bidders with lower cognitive ability whereas it has little or even adverse effects for higher-ability bidders.

First Price Sealed-Bid Auctions with Bidders’ Heterogeneous Risk Behavior: An Adversarial Risk Analysis Approach

Bidders’ bidding behavior is analyzed in first price sealed-bid (FPSB) auctions using an adversarial risk analysis (ARA) framework. However, using nonstrategic play and level-k thinking solution concepts, modeling is performed by assuming only two bidders. Also, the aleatory and concept uncertainties have not been yet taken into account by using an ARA framework for these auctions. In this paper, we apply an ARA approach to model bidders’ bidding behavior in a more realistic way for FPSB auctions. We assume n bidders that may have different wealth and heterogeneous risk behaviors. We use nonstrategic play and level-k thinking solution concepts, and we take into account aleatory uncertainty in addition to epistemic uncertainty. Finally, concept uncertainty is taken into account to find ARA solutions for these auctions. We also provide numerical examples to illustrate our methodology.

A functional estimation approach to the first-price auction models

This paper introduces new methods of identification and estimation of the first-price sealed bid auction model and compares them with the previous existing ones.The first method of estimation allows us to estimate directly (through an iterative algorithm) the cumulative distribution function of the private values without estimating the private values beforehand. In the second method, we use a quantile approach. Although the first-price auction is a complex nonlinear inverse problem, the use of quantile leads to a linearization of the model. Thus, in contrast with the existing methods we are able to deduce a closed-form solution for the quantile of the private values. This constructive identification allows for a one-stage estimation procedure that can be performed using three regularization methods: the Tikhonov regularization, the Landweber–Friedman regularization and the kernels.We conduct a Monte Carlo experiment to compare our methods of estimation by c.d.f. and quantiles with the methods of estimation developed by Guerre et al. (2000), Marmer and Shneyerov (2012), and Hickman and Hubbard (2015).Some extensions of the model are considered: asymmetric bidders, affiliation, conditional models to exogenuous variables, and the observation of only the winning bids.

On the Complexity of Equilibrium Computation in First-Price Auctions

We consider the problem of computing a (pure) Bayes-Nash equilibrium in the first-price auction with continuous value distributions and discrete bidding space. We prove that when bidders have independent subjective prior beliefs about the value distributions of the other bidders, computing an $\varepsilon$-equilibrium of the auction is PPAD-complete, and computing an exact equilibrium is FIXP-complete. We also provide an efficient algorithm for solving a special case of the problem, for a fixed number of bidders and available bids.

When Will First-Price Work Well? The Impact of Anti-Corruption Rules on Photovoltaic Power Generation Procurement Auctions

Along with the prevalence of photovoltaic (PV) procurement contracts, the corruption between auctioneers and potential electricity suppliers has attracted the attention of energy regulators. This study considers a corruption-proof environment wherein corruption is strictly suppressed. It elaborates a mechanism to explore the impact of corruption-proof measures on PV procurement auctions. It adopts incentive compatible constraints based on revelation principle to reflect PV firms’ optimal utilities. It employs first-price and first-score auctions and uses the Bayesian Nash equilibrium to provide a description of market outcomes. The results show that several strategies have different impacts on social welfare, PV firms’ utility, and the benefits of corruption. First, a first-price auction cannot act as a suitable policy because it may encourage corruption. Second, the first-score choice is desirable for social welfare to fit the forthcoming high-quality and low-price surroundings. Third, the first-score strategy maximizes PV firms’ utility and total income. The implications suggest that regulators ought not to employ first-price auctions in the future PV market from the perspective of social welfare. Another disadvantage of the first-price approach is that it enables the PV firm to maintain the utmost benefit from corruption.

Correction: Computing Profit-Maximizing Bid Shading Factors in First-Price Sealed-Bid Auctions

Correction: Computing Profit-Maximizing Bid Shading Factors in First-Price Sealed-Bid Auctions

Auction Pricing Mechanism of Construction Land Quota Based on Preference

In order to study the impact of the location preference of construction land on the auction pricing strategy of construction land quota, this study constructs a first-price auction and two-price auction model for bidders participating in the construction land quota and construction land auction based on the sequential auction theory. Therefore, the role of preference is discussed, and finally the conclusion is verified by an example. The results show that under the two auction modes, preference has a positive impact on the bidding strategy of construction land quota and farmers’ expected income. Compared with sequential first-price auction, the bidding strategy of sequential second-price auction is more competitive, and the quota equilibrium bidding price and farmers’ income obtained are higher.

CoMCLOUD: Virtual Machine Coalition for Multi-Tier Applications Over Multi-Cloud Environments

Applications hosted in commercial clouds are typically multi-tier and comprise multiple tightly coupled virtual machines (VMs). Service providers (SPs) cater to the users using VM instances with different configurations and pricing depending on the location of the data center (DC) hosting the VMs. However, selecting VMs to host multi-tier applications is challenging due to the trade-off between cost and quality of service (QoS) depending on the placement of VMs. This paper proposes a multi-cloud broker model called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CoMCLOUD</i> to select a sub-optimal VM coalition for multi-tier applications from an SP with minimum coalition pricing and maximum QoS. To strike a trade-off between the cost and QoS, we use an ant-colony-based optimization technique. The overall service selection game is modeled as a first-price sealed-bid auction aimed at maximizing the overall revenue of SPs. Further, as the hosted VMs often face demand spikes, we present a parallel migration strategy to migrate VMs with minimum disruption time. Detailed experiments show that our approach can improve the federation profit up to 23% at the expense of increased latency of approximately 15%, compared to the baselines.

A Bayesian equilibrium for simultaneous first-price auctions for complementary goods and quasi-linear bids

&lt;p style='text-indent:20px;'&gt;This article shows a Symmetrical Bayesian Nash Equilibrium in a context of &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;\begin{document}$ m $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt; simultaneous first-price sealed-bid auctions and &lt;inline-formula&gt;&lt;tex-math id="M2"&gt;\begin{document}$ n $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt; bidders for complementary goods. We consider that the individual valuations of the &lt;inline-formula&gt;&lt;tex-math id="M3"&gt;\begin{document}$ m $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt; goods are common knowledge and identical among bidders and if the whole set of goods is gained, a private independent extra profit is obtained by the winner. For relaxing and solving the so-many mathematical complications involved in the general case we followed a classical methodology and proposed a particular bidding function that implies linear separability. Under this assumptions we obtain a Symmetric Bayesian Nash Equilibrium which functional form implies the classic quasi-linear property for bivariate functions. On addition, we compare the seller expected revenue between auctioning the complete set in one single first-price sealed-bid auction versus auctioning each item in &lt;inline-formula&gt;&lt;tex-math id="M4"&gt;\begin{document}$ m $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt; simultaneous first-price sealed-bid auctions.&lt;/p&gt;

Entry in first-price auctions with signaling

We study the optimal entry fee in a symmetric private value first-price auction with signaling, in which the participation decisions and the auction outcome are used by an outside observer to infer the bidders’ types. We show that this auction has a unique fully separating equilibrium bidding function. When the bidders’ sensibility for the signaling concern is sufficiently strong, the expected revenue maximizing entry fee is the maximal fee that guarantees full participation. The larger is the bidder’s sensibility, the higher is the optimal participation.

Market Design for AI Algorithms

We discuss results from a few recent papers on how market design affects play between artificial intelligence (AI) algorithms. We describe the results from Banchio and Skrzypacz [2022] where the first-price auction appears more prone to collusion than the second-price auction. We also discuss results showing that information feedback after the auction, which allows computation of counterfactual payoffs, can improve competition.

Settling the Efficiency of the First-Price Auction

We survey the main result from [Jin and Lu 2022]: For the first-price auction, the tight Price of Anarchy is 1 - 1/e 2 ≈ 0.8647, which closes the gap between the best known bounds [0.7430, 0.8689].

Separating probability weighting and risk aversion in first-price auctions

In first price sealed-bid auctions, a power probability weighting function is observationally equivalent to a model with constant relative risk aversion. By comparing auctions with different ceilings on a computerized opponent’s bid space, we can separate inverse S-shaped probability weighting as commonly used in the literature and risk-averse preferences from the distribution of observed bids. We find evidence to support both theories in the data. However, we also observe a significant number of violations after accounting for decision noise, which suggest that bidders’ valuations may be malleable to cues of the auction environment. • We design an experiment to separate probability weighting and risk-aversion in bidding. • We vary the beliefs about the opponent without changing the risk neutral optimal bid. • We find evidence to support both probability weighting and risk aversion in the data. • We observe a significant number of violations of both probability weighting and risk aversion. • We find that bidders’ valuations may be malleable to cues of the auction environment.

Real Time Auction Models for Programmatic Advertising Efficiency

The rapid evolution of programmatic advertising has necessitated the development of real-time auction models to enhance efficiency and optimize ad spend. This study explores the dynamics of real-time auctions within programmatic advertising, focusing on the mechanisms that drive bid strategies and pricing models. By analyzing the interplay between advertisers, publishers, and demand-side platforms (DSPs), we identify the factors influencing bidding behavior and auction outcomes. We propose a novel framework that integrates machine learning algorithms to predict bid values based on historical data and contextual parameters, aiming to improve decision-making processes in real-time environments. Furthermore, this research examines the impact of auction transparency and competition on advertising effectiveness, revealing how different auction formats—such as second-price and first-price auctions—affect bidder strategies and overall campaign performance. We employ empirical analysis using data from various programmatic platforms to validate our model, demonstrating significant improvements in cost efficiency and ad placement outcomes. Ultimately, our findings contribute to a deeper understanding of real-time auction dynamics in programmatic advertising, providing actionable insights for marketers seeking to enhance campaign efficiency. By leveraging advanced analytics and real-time data, advertisers can better navigate the complexities of programmatic ecosystems, resulting in optimized advertising strategies that maximize return on investment (ROI) while effectively engaging target audiences.