Auction Design Research Articles

Optimal Auctions through Deep Learning: Advances in Differentiable Economics

Designing an incentive compatible auction that maximizes expected revenue is an intricate task. The single-item case was resolved in a seminal piece of work by Myerson in 1981, but more than 40 years later, a full analytical understanding of the optimal design still remains elusive for settings with two or more items. In this work, we initiate the exploration of the use of tools from deep learning for the automated design of optimal auctions. We model an auction as a multi-layer neural network, frame optimal auction design as a constrained learning problem, and show how it can be solved using standard machine learning pipelines. In addition to providing generalization bounds, we present extensive experimental results, recovering essentially all known solutions that come from the theoretical analysis of optimal auction design problems and obtaining novel mechanisms for settings in which the optimal mechanism is unknown.

Implementation in undominated strategies with applications to auction design, public good provision and matching

This paper considers implementation in undominated strategies by finite mechanisms, where multiple outcomes may be implemented at a single state of the world. We establish a sufficient condition for implementation applicable in a general environment with private values. We apply it to three well-known environments and obtain strikingly permissive results. In the single-object auction, the second-price auction with a reserve price can be outperformed in terms of revenue. In the public good provision problem, the Vickrey–Clarke–Groves mechanism can be outperformed from the viewpoint of a designer who wishes to minimise deficit subject to efficiency. In the two-sided matching environment where preferences on one side of the market are private information, the social choice correspondence that outputs all stable matchings at every preference profile, is implementable.

Quantile analysis of “hazard-rate” game models

This paper consists of an econometric analysis of a broad class of games of incomplete information. In these games, a player’s action depends both on her unobservable characteristic (the private information), as well as on the ratio of the distribution of the unobservable characteristic and its density function (which we call the ”hazard-rate”). The goal is to use data on players’ actions to recover the distribution of private information. We show that the structural parameter (the quantile of the unobservable characteristic, denoted by L) can be related to the reduced form parameter (the quantile of the data, denoted by Q) through a differential equation Q(α)=a(L(α),αL′(α)). We analyse the local and global identification of this equation in L. At the same time, under suitable assumptions, we establish the local and global well-posedness of the inverse problem Q=T(L). We solve the differential equation and, as a consequence of the well-posedness, we estimate nonparametrically the quantile and the c.d.f. function of the unobserved variables at a root-n speed of convergence (conditional on the quantile of the data being estimated at root-n). Moreover as the transformation of Q in L is continuous with respect to a topology that implies also the derivatives, we estimate nonparametrically the quantile density and the density the unobserved variables (that are continuous functions with respect to Q) at root-n speed of convergence. We provide also several generalisations of the model accounting for exogenuous variables, implicit expression of the strategy function and integral expression of the strategy function. Our results have several policy applications, including better design of auctions, regulation models, estimation of war of attrition in patent races, and public good contracts.

Auction design with data‐driven misspecifications: Inefficiency in private value auctions with correlation

We study the existence of efficient auctions in private value settings in which some bidders form their expectations about the distribution of their competitor's bids based on the accessible data from past similar auctions consisting of bids and ex post values. We consider steady states in such environments with a mix of rational and data‐driven bidders, and we allow for correlation across bidders in the signal distributions about the ex post values. After reviewing the working of the approach in second‐price and first‐price auctions, we establish our main result that there is no efficient auction in such environments.

Diffusion auction design with transaction costs

Diffusion auction design with transaction costs

Analysing the impact of renewable energy auctions on market concentration

An abundant literature on the advantages and drawbacks of different auction design elements exists. However, their comparative effects on market concentration have not been explored, despite the increasing concern of governments about this issue. This article covers this gap in the literature. It follows an exploratory approach to provide a better understanding of the relationship between auctions, design elements and market concentration. An analytical framework is developed to assess the effects of auction and auction design elements on two aspects of market concentration (number and diversity of firms). Then, some research proposals are inferred from this framework and illustrated with a case study of wind power in Spain. Data have been collected through an expert elicitation survey and a Multi-criteria Analysis has been performed. The results show that, compared to administratively-set remuneration, auctions increase market concentration. Furthermore, their impact on market concentration is mediated by the choice of specific design elements (the existence of a schedule, the remuneration type and stringent prequalification requirements). However, those effects of auctions and their design elements are relatively low compared to other context factors. Therefore, if the aim is to reduce market concentration, policy makers should improve these context conditions, followed by auction design.

Empirical evidence on discrimination in multi-technology renewable energy auctions in Europe

Auctions are a widely used policy instrument to support the deployment of renewable energies (RE). Yet, their complex design raises concerns about explicitly or implicitly discriminatory effects against particular technologies. Such discriminatory effects would distort fair competition, reduce economic efficiency, and potentially violate European Union law.Several studies analysed discriminatory auction design from a theoretical and simulation perspective but actual empirical evidence is limited. Here, we demonstrate the existence of technology discrimination in European RE auctions empirically. We apply a fractional logit model to empirically measure the impact of various auction design elements on the success of two technologies, solar PV and onshore wind, based on 57 European multi-technology RE auctions from 2011–2021.Our results confirm the existence of discriminatory effects of several auction design elements in RE auctions, such as installation size restriction, support duration, realisation period, ceiling price, and financial prequalification. The results are stable against various robustness checks such as varying the countries included, the time frame, and the composition of the regions controlled for.Our findings advance the understanding of explicitly and implicitly discriminatory effects against particular technologies in multi-technology auctions and we propose steps to reduce technology discrimination in future multi-technology RE auctions.

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 practical multi-objective auction design and optimization framework for sponsored search

We propose a simple, flexible, efficient, and general framework for running large-scale highly-dynamic sponsored search auctions. Our framework aims at exploring optimal tradeoffs among various objectives of three parties: platform, advertisers, and users. We model the optimal tradeoffs as an online linear program problem, which can be addressed by a simple approach based on semi-Lagrangian duality. Experimental results conducted on large-scale real-world traffic show that the proposed framework can significantly improve all objectives considered, as well as the platform's revenue.

Energy Storage Sharing for Multiple Services Provision: A Computable Combinatorial Auction Design

Given the profound integration of the sharing economy and the energy system, energy storage sharing is promoted as a viable solution to address the underutilization of energy storage and the challenges associated with cost recovery. While energy storage sharing offers various services for system operation, a significant question remains regarding the development of an optimal allocation model for shared energy storage in diverse application scenarios and the proposal of efficient solving algorithms. This paper presents the design of a computable combinatorial mechanism aimed at facilitating energy storage sharing. Leveraging the distinct characteristics of buyers and sellers engaged in energy storage sharing, we propose a combinatorial auction solving algorithm that prioritizes and incorporates the offers of shared energy storage, accounting for temporal variations in the value of energy resources. The numerical results demonstrate that the proposed solving algorithm achieves a computation time reduction of over 95%, adequately meeting the practical requirements of industrial applications. Importantly, the proposed method maintains a high level of computational accuracy, ranging from 92% to 98%, depending on the participants and application scenarios. Hopefully, our work is able to provide a useful reference for the further mechanism design for energy storage sharing.

Land use impacts of the Conservation Reserve Program: An analysis of rejected offers

AbstractThe Conservation Reserve Program is the largest agricultural land retirement program in the United States, with more enrolled acreage entering the program through a competitive auction called the General Signup than any other component. In this study, we assess the land use impacts of the Conservation Reserve Program by observing the land use decisions of parcels following the 2016 General Signup. We estimate land use impacts using a regression discontinuity design based on the Environmental Benefits Index, the program's selection and ranking mechanism. Our estimates largely rely on the auction design of the General Signup, such that we observe the land use decisions of rejected offers. We also use information on the rental rates of these offers to understand what the program pays to retire land in different uses. We estimate that a marginal acre of land enrolled in the Conservation Reserve Program replaces 0.30 acres in cropland, 0.25 acres in mixed forage, 0.32 acres in grassland, 0.12 acres in idle or fallow land, and 0.01 acres in timberland. We also find that enrollments from newly offered fields are more likely to displace cropland and less likely to displace grassland than returning fields. Consequently, we estimate that new enrollments lead to 47% greater reductions in water‐driven erosion and 12% greater reductions in wind‐driven erosion, compared to fields with prior enrollment.

Auction design by an informed seller: A foundation of reserve price signalling

AbstractThis paper studies mechanism design by a seller privately informed of the (continuous) quality of an indivisible object. An important solution to this informed‐principal problem, the Rothschild–Stiglitz–Wilson mechanisms, which correspond to the least‐cost separating allocations in the signalling literature, is characterized. The characterization reveals that reserve prices are the least costly device to separate sellers of different qualities: In the RSW mechanisms, the lowest‐quality seller adopts her public‐information optimal selling procedure, and each higher‐quality seller adopts a selling procedure that differs from her public‐information optimal one only in that the reserve prices are higher. This finding provides a mechanism‐design foundation for reserve‐price signalling studied in the literature.

Carbon allowance auction design of China's ETS: A comprehensive hierarchical system based on blockchain

This study proposes a blockchain-based optimization framework for carbon allowance allocation auctions. First, the study assesses the status quo of carbon trading, pinpointing barriers, future development trends, and identifying carbon quota auction standards and methods pertinent to the Chinese context. Second, based on China's carbon market needs and the technical characteristics of blockchain, this study reconfigures the functions and responsibilities of each participant and creates a framework for a carbon allowance auction system to optimize the carbon trading process. Third, an algorithm for the carbon allowance auction system is constructed, and the corresponding smart contract is created and simulated. The results illustrate that our proposed system framework facilitates universal carbon allowance auctions, efficiently addresses potential disputes during the auction process, enhances market transparency and credibility, and offers comprehensive privacy protection with flexible information disclosure options for corporations. Blockchain's role in fostering paid distribution and incentivizing participation in the carbon market is further recognized. A blockchain-based carbon trading system safeguards transaction security and efficiency, maintains precise transaction records, and provides automated settlement. Ultimately, this paper presents policy suggestions for the development of a national carbon market in China.

Can auctions increase competition in the pension funds market? The Chilean experience

This paper analyses the auction policy over enrollees’ monopoly rights introduced in the Chilean pension system. This policy was designed to promote competition in the pension fund market driven by private firms, after 30 years of operation. Since the Chilean pension fund system has inspired dozens of countries in the last forty years, the analysis of the design and performance of its relatively new auction mechanism is of worldwide interest. We present a theoretical and empirical model. Our theoretical model illustrates firms’ incentives to participate in the auction process. Our empirical analysis focuses on the effect of auctions on outcomes, such as fees, mark-ups, demand price elasticity, returns, and risk premiums. Despite the evidence shown for the positive benefits of the auction implementation, the current mechanism design is not considering that the biggest issue is the low individuals’ price response levels. Importantly, the current auction design only incentivizes new entrants to participate. Thus, the design generates low competition in the auction processes. Proper design should incentivize all firms to participate. Besides, we find that consumers’ price elasticity increased after the implementation of auctions, although demand is still generally inelastic. Interestingly, non-winning auction firms did not react in fees but may have reacted in other characteristics, such as returns and risk premiums.

Blending Advertising with Organic Content in E-commerce via Virtual Bids

It has become increasingly common that sponsored content (i.e., paid ads) and non-sponsored content are jointly displayed to users, especially on e-commerce platforms. Thus, both of these contents may interact together to influence their engagement behaviors. In general, sponsored content helps brands achieve their marketing goals and provides ad revenue to the platforms. In contrast, non-sponsored content contributes to the long-term health of the platform through increasing users' engagement. A key conundrum to platforms is learning how to blend both of these contents allowing their interactions to be considered and balancing these business objectives. This paper proposes a system built for this purpose and applied to product detail pages of JD.COM, an e-commerce company. This system achieves three objectives: (a) Optimization of competing business objectives via Virtual Bids allowing the expressiveness of the valuation of the platform for these objectives. (b) Modeling the users' click behaviors considering explicitly the influence exerted by the sponsored and non-sponsored content displayed alongside through a deep learning approach. (c) Consideration of a Vickrey-Clarke-Groves (VCG) Auction design compatible with the allocation of ads and its induced externalities. Experiments are presented demonstrating the performance of the proposed system. Moreover, our approach is fully deployed and serves all traffic through JD.COM's mobile application.

Resolving Failed Banks: Uncertainty, Multiple Bidding and Auction Design

Abstract The FDIC resolves insolvent banks with scoring auctions. Although the structure of the scoring rule is known to bidders, they are uncertain about how the FDIC trades off different bid components. Scoring-rule uncertainty motivates bidders to submit multiple bids for the same failed bank. To evaluate the effects of uncertainty and multiple bidding for FDIC costs, we develop a methodology for analysing multidimensional bidding when the auctioneer’s scoring weights are unknown to bidders. We estimate private valuations for failed-bank assets during the great financial crisis and compute counterfactuals in the absence of scoring uncertainty. Our findings imply a substantial reduction in FDIC resolution costs of between 29.8% ($8.2 billion) and 44.6% ($12.3 billion). These savings can reduce policy-driven banking-sector distortions, since FDIC resolution costs are covered either through special levies on banks or through loans from the US Treasury. Our analyses also shed new light on optimal bid portfolio choice in combinatorial auctions.

Optimal Bidder Selection in Clearing House Default Auctions

Default auctions at central counterparties (or ‘CCPs’) are critically important to financial stability. However, due to their unique features and challenges, standard auction theory results do not immediately apply. This paper presents a model for CCP default auctions that incorporates the CCP’s non-standard objective of maximizing success above a threshold rather than revenue, the key question of who participates in the auction and the potential for information leakage affecting private portfolio valuations. We show that an entry fee, by appropriately inducingmembers to participate or not, can maximize the probability the auction succeeds. The result is novel, both in auction theory and as a mechanism for CCP auction design.

Auction design with shortlisting when value discovery is covert

This paper studies optimal auction design when buyers’ value discovery investment is covert but essential for mutually beneficial trade between seller and buyers. Since selling mechanisms contingent on value discovery (e.g. ex-ante examination fees charged upon information acquisition) are not feasible, we focus mainly on second price auctions with reserves, which can be contingent on the number of actual bidders ex-post. Under a regularity condition of monotone hazard rate, we find that the optimal reserve depends on the number of shortlisted bidders, but for any given shortlist it does not depend on the number of actual bidders. Depending on the value discovery cost, the seller shortlists either the socially efficient number of buyers or one more bidder. The comparison between the two options of the seller is completely resolved. The optimal reserve depends discontinuously and non-monotonically on the value discovery cost. In the former case, equilibrium information acquisition is efficient but ex-post allocation is inefficient, while in the latter case, it is the opposite.

A Semi-supervised Sensing Rate Learning based CMAB scheme to combat COVID-19 by trustful data collection in the crowd

The recruitment of trustworthy and high-quality workers is an important research issue for MCS. Previous studies either assume that the qualities of workers are known in advance, or assume that the platform knows the qualities of workers once it receives their collected data. In reality, to reduce costs and thus maximize revenue, many strategic workers do not perform their sensing tasks honestly and report fake data to the platform, which is called False data attacks. And it is very hard for the platform to evaluate the authenticity of the received data In this paper, an incentive mechanism named Semi-supervision based Combinatorial Multi-Armed Bandit reverse Auction (SCMABA) is proposed to solve the recruitment problem of multiple unknown and strategic workers in MCS. First, we model the worker recruitment as a multi-armed bandit reverse auction problem and design an UCB-based algorithm to separate the exploration and exploitation, regarding the Sensing Rates (SRs) of recruited workers as the gain of the bandit Next, a Semi-supervised Sensing Rate Learning (SSRL) approach is proposed to quickly and accurately obtain the workers’ SRs, which consists of two phases, supervision and self-supervision. Last, SCMABA is designed organically combining the SRs acquisition mechanism with multi-armed bandit reverse auction, where supervised SR learning is used in the exploration, and the self-supervised one is used in the exploitation. We theoretically prove that our SCMABA achieves truthfulness and individual rationality and exhibits outstanding performances of the SCMABA mechanism through in-depth simulations of real-world data traces.

The impact of competition, trust and capital on renewable energy auction outcomes in sub-Saharan Africa: Analysing auctions in South Africa, Zambia and Namibia

Africa is short of power, despite having abundant renewable energy resources. Over the past decade, renewable energy auctions have emerged as an effective mechanism to competitively procure utility-scale private power projects. This paper identifies the elements contributing to efficient price and effective project realisation outcomes through comparative case studies in South Africa, Zambia and Namibia. The analysis combined existing literature and theory on those elements that contribute to success in Independent Power Projects (IPPs), with that on renewable energy auction design and implementation. The application of an integrated analytical framework shows that the introduction of renewable energy auctions in Africa provides an essential programmatic element which connects existing country and project level factors and is crucial in achieving superior project realisation and price outcomes, compared to projects procured through direct negotiation or feed-in tariffs.Auction price outcomes are mainly determined by factors that act as auction signals, barriers and incentives primarily geared towards increasing competition in the procurement process and lowering projects' cost of capital. The case studies also show that project realisation is determined by bidder quality, project preparation levels, investor commitment, constraints (revenue stream and political economy) and post-award support. These are influenced by factors from all three levels – country, project and programme – that act as auction signals, barriers, incentives and support measures. Factors influencing bidders’ trust in the auctioning authority and auction process are particularly important signals influencing both project prices and realisation rates.