Single-unit Auctions Research Articles

Information design in optimal auctions

We study the information design problem in a single-unit auction setting. The information designer controls independent private signals according to which the buyers infer their binary private values. Assuming that the seller adopts the optimal auction due to Myerson (1981) in response, we characterize both the buyer-optimal information structure, which maximizes the buyers' surplus, and the seller-worst information structure, which minimizes the seller's revenue. We translate both information design problems into finite-dimensional, constrained optimization problems in which one can explicitly solve for the optimal information structure. In contrast to the case with one buyer (Roesler and Szentes, 2017), we show that with two or more buyers, the symmetric buyer-optimal information structure is different from the symmetric seller-worst information structure. The good is always sold under the seller-worst information structure but not under the buyer-optimal information structure. Nevertheless, as the number of buyers goes to infinity, both symmetric information structures converge to no disclosure. We also show that in our ex ante symmetric setting, an asymmetric information structure is never seller-worst but can generate a strictly higher surplus for the buyers than the symmetric buyer-optimal information structure.

Bidder Support in Multi-item Multi-unit Continuous Combinatorial Auctions: A Unifying Theoretical Framework

Combinatorial auctions have seen limited applications in large-scale consumer-oriented marketplaces, partly due to the substantial complexity to keep track of auction status and formulate informed bidding strategies. We study the bidder support problem for the general multi-item multi-unit (MIMU) combinatorial auctions, where multiple heterogeneous items are being auctioned and multiple homogeneous units are available for each item. Under two prevalent bidding languages (OR bidding and XOR bidding), we derive theoretical results and design efficient algorithmic procedures to calculate important bidder support information, such as the winning bids of an auction and the minimum bidding value for a bid to win an auction either immediately or potentially in the future. Our results unify the theoretical insights on bidder support problem for different bidding languages as well as different special cases of general MIMU auctions, namely the single-item multi-unit (SIMU) auctions and the multi-item single-unit (MISU) auctions. We also consider auctions with additional bidding constraints, including batch-based combinatorial auctions and hierarchical combinatorial auctions, as well as the combinatorial reverse auctions, all of which have relevant practical applications (e.g., industrial procurements). Our results can be readily extended to solve the bidder support problems in these auction mechanisms.

Auction theory and a note on game mechanisms

Abstract This paper will review important topics on the subject of auction theory and mechanism design, these include: efficiency first and foremost, also revenue comparison between different types of auctions and the issue of incentive compatibility, individual rationality with the general idea and proof that bilateral trade is inefficient. Mechanism design theory tells us that if buyers and sellers both have private information full efficiency is impossible, however Vickrey auction (single unit auction) will be efficient i.e. will put the goods in the hands of the buyers that value them most. However, the conclusion from this paper is that because of overvaluation of bidders the main result is inefficient, i.e. bids are too high. When weak and strong bidders are compared the main conclusion is that strong bidders’ expected payoff is higher in second price auction (SPA), while weak bidder prefers first price auction (FPA) bid.

The effects of bidder factors on online bidding strategies: A motivation-opportunity-ability (MOA) model

The use and popularity of online auctions is growing all over the world. Bidding strategies are important because they are related to an auction's final price and ultimately its revenue. This study investigates the bidding strategies adopted by online bidders and the factors of the bidders, including bidding motivations, time availability, bidding experience, and risk aversion. We use the data from China to test the model and identify three bidding strategies in single-unit auctions: agent bidding, snipe bidding, and ratchet bidding. By running logistic regression, we find that hedonic motivations, utilitarian motivations, time availability, bidding experience, and risk preference all influence online bidding strategies. We also conduct pairwise comparisons of bidding strategies based on these factors and a simulation experiment to compare the benefits brought by different bidding strategies. We conclude by discussing the implications for both research and practice.

The Effects of Bidder Factors on Online Bidding Strategies: A Motivation-Opportunity-Ability (MOA) Model

The use and popularity of online auctions is exploding all over the world. Bidding strategies are important because they are related to an auction’s final price and ultimately its revenue. This study investigates the bidding strategies adopted by online bidders and the factors of the bidders, including bidding motivations, time availability, bidding experience, and risk aversion. We use the data from China to test the model and identify three bidding strategies in single-unit auctions: agent bidding, snipe bidding, and ratchet bidding. By running logistic regression, we find that hedonic motivations, utilitarian motivations, time availability, bidding experience, and risk preference all influence online bidding strategies. We also conduct pairwise comparisons of bidding strategies based on these factors and a simulation experiment to compare the benefits brought by different bidding strategies. We conclude by discussing the implications for both research and practice.

How Efficient are Decentralized Auction Platforms?

Abstract We model a decentralized, dynamic auction market platform in which a continuum of buyers and sellers participate in simultaneous, single-unit auctions each period. Our model accounts for the endogenous entry of agents and the impact of intertemporal optimization on bids. We estimate the structural primitives of our model using Kindle sales on eBay. We find that just over one-third of Kindle auctions on eBay result in an inefficient allocation with deadweight loss amounting to 14% of total possible market surplus. We also find that partial centralization—for example, running half as many 2-unit, uniform-price auctions each day—would eliminate a large fraction of the inefficiency, but yield lower seller revenues. Our results also highlight the importance of understanding platform composition effects—selection of agents into the market—in assessing the implications of market redesign. We also prove that the equilibrium of our model with a continuum of buyers and sellers is an approximate equilibrium of the analogous model with a finite number of agents.

Information Design in Optimal Auctions

We study the information design problem in a single-unit auction setting. The information designer controls independent private signals according to which the buyers infer their binary private value. Assuming that the seller adopts Myerson (1981) optimal auction in response, we characterize both the buyer-optimal information structure which maximizes the buyers' surplus and the seller-worst information structure which minimizes the seller's revenue. We translate both information design problems into finite-dimensional constrained optimization problems for which the optimal information structures can be explicitly solved. In contrast to the case with one buyer (Roesler and Szentes, 2017 and Du, 2018), we show that with two or more buyers, the buyer-optimal information structure is different from the seller-worst information structure: the good is always sold under the seller-worst information structure but not under the buyer-optimal information structure. Nevertheless, as the number of buyers goes to infinity, both information structures converge to no disclosure. We also show that in an ex ante symmetric setting, an asymmetric information structure is never seller-worst but for some prior can generate a strictly higher surplus for the buyers than the symmetric buyer-optimal information structure.

T-Tree: The Tokyo toolbox for large-scale combinatorial auction experiments

This paper provides a brief introduction to t-Tree, a general auction software package that implements single-unit auctions, Vickrey–Clarke–Groves auctions (“VCG auctions”), Simultaneous Multiple Round Auctions (“SMRA”), and Combinatorial Clock Auctions (“CCA”) used in transportation, logistics, procurements, and spectrum allocation. The critical contribution of t-Tree is that it can handle computational complexities of the winner determination problem in large-scale combinatorial auctions by natively implementing Zhong et al. (2004)’s combinatorial optimization algorithms. Thus researchers can study large-scale combinatorial auction mechanisms off the shelf using t-Tree.

Robustly Optimal Reserve Price

We study a robust version of the single-unit auction problem. The auctioneer has confidence in her estimate of the marginal distribution of a generic bidder's valuation, but does not have reliable information about the joint distribution. In this setting, we analyze the performance of second-price auctions with reserve prices in terms of revenue guarantee, that is, the greatest lower bound of revenue across all joint distributions that are consistent with the marginals. For any finite number of bidders, we solve for the robustly optimal reserve price that generates the highest revenue guarantee. Our analysis has interesting implications in large markets. For any marginal distribution, the robustly optimal reserve price converges to zero as the number of bidders gets large. Furthermore, the second-price auction with no reserve price is asymptotically optimal among all mechanisms.

Supply function competition with asymmetric costs: Theory and experiment

We study a multi-unit auction, where bidders differ in their marginal costs, and compare the outcome to the Bertrand (or single-unit auction) analogue.

Revisiting the foundations of dominant-strategy mechanisms

An important question in mechanism design is whether there is any theoretical foundation for the use of dominant-strategy mechanisms. This paper studies the maxmin and Bayesian foundations of dominant-strategy mechanisms in general social choice environments with quasi-linear preferences and private values. We propose a condition called the uniform shortest-path tree that, under regularity, ensures the foundations of dominant-strategy mechanisms. This exposes the underlying logic of the existence of such foundations in the single-unit auction setting, and extends the argument to cases where it was hitherto unknown. To prove this result, we adopt the linear programming approach to mechanism design. In settings in which the uniform shortest-path tree condition is violated, maxmin/Bayesian foundations might not exist. We illustrate this by two examples: bilateral trade with ex ante unidentified traders and auction with type-dependent outside option.

Optimal Deterministic Mechanism Design: Type-Independent Preference Orderings

We investigate revenue maximisation in general allocation problems with incomplete information, where we assume quasi-linearity, private values, independent type distributions and single-dimensionality of type spaces. We require a mechanism to be deterministic, strategy-proof and ex-post individually rational. We assume that each player has a type-independent preference ordering over deterministic allocations. We show that the Myerson’s technique to solve the incentive-constrained revenue maximisation problem in single-unit auctions can be applied to general allocation problems, where the incentive-constrained revenue maximisation problem can be reduced to the simple maximisation problem of the sum of players’ virtual valuations without imposing any incentive constraint.

On the Failure of the Linkage Principle with Colluding Bidders

One of the fundamental results of auction theory is the Linkage Principle, which states that the seller’s expected revenue is enhanced by ex ante full public disclosure of information about the value of the good. Previous literature has established that the Principle fails in dynamic settings. We argue that information provision may also sustain collusion in single-unit auctions, thus harming the auctioneer. Using a model with private and common value components, we point out that disclosure curtails common value uncertainty, making communication between cartel members incentive compatible. We also show that collusion is feasible if and only if information provision reaches an interior threshold value.

Bidding Behavior in Dutch Auctions: Insights from a Structured Literature Review

ABSTRACTThe Dutch auction, also known as the descending-price auction or reverse clock auction, has a long-standing history in practice and in academic literature. In practice, the Dutch auction is commonly used to rapidly sell large quantities of homogeneous goods, such as cut flowers, fish, or tobacco. However, most e-commerce auction sites focus on other auction mechanisms, and overall research on human behavior in Dutch auctions is scant. To facilitate research on Dutch auctions and their applications in electronic commerce, we conduct a structured literature review of experimental studies and establish the current state of research on bidding behavior in single-unit and multi-unit Dutch auctions. The findings are based on an analysis of twenty-nine articles published in the fields of economics, information management, marketing, and operations research and management science between 1970 and 2016. This review reveals (1) the characteristics that make the Dutch auction unique compared to other auction formats, (2) the drivers of bidding behavior in Dutch auctions, and (3) an overview of how Dutch auctions can be employed in practice and to what advantage. Finally, we identify directions for future research on bidding behavior in Dutch auctions.

Auction cartels and the absence of efficient communication

This paper examines the feasibility of collusive mechanisms in single-unit auctions. A model is constructed with private and common value information asymmetry and continuous type space. We show that an incentive compatible bid coordination mechanism (BCM) does not exist if common value uncertainty is present. This result contradicts actual antitrust cases, where common effects or resale opportunities created uncertainty about valuations, but a price-fixing cartel was formed. We solve the puzzle by relaxing the assumption that all bidder types truthfully reveal their private information. The introduced Bayesian bid coordination mechanism (BBCM) exists if the main source of information asymmetry is private value. In that case, a designated ring member can signal high valuation and suppress competition. Our results demonstrate the rationale behind cartel mechanisms with pre-auction knockouts.

Optimal Quantity Caps in Discriminatory Price Auctions with Resale

We present a model of a discriminatory price auction in which a large bidder competes against many small bidders, followed by a post-auction resale stage in which the large bidder is endogenously determined to be a buyer or a seller. We extend the first-price auction with resale results of Hafalir and Krishna (2008) to this setting and give a tractable characterization of equilibrium behavior. We use this to study the policy of capping the amount that may be won by large bidders in the auction. Despite being used in the US Treasury auction among others, this policy has received little attention in the auction literature. Our analysis shows that the trade-offs involved when adjusting these quantity caps can be understood in terms familiar to students of asymmetric first-price single unit auctions. Furthermore, whether one seeks to maximize revenue or efficiency has stark and contradictory implications for the choice of cap.

Agent-based simulation of multiple-round timber combinatorial auction

This paper presents a simulation-based analysis of a multiple-round timber combinatorial auction in the timber industry. Currently, most timber auctions are single-unit auctions (i.e., each forest stand is sold separately). However, other types of auctions could be applied to take advantage of the various needs of the bidders with respect to species, volumes, and quality. This study aims to analyze the use of combinatorial auction to this specific context using a simulation approach. Various number of auctions per year, periodicity, lot size, and number of bidders are considered as parameters to set up the different market configurations. The outcomes of both combinatorial auction and single-unit auction are compared with respect to different setup configurations. This analysis shows that combinatorial auction can bring more profit for both seller and buyer when the market is less competitive.

How Efficient are Decentralized Auction Platforms?

We provide a model of a decentralized, dynamic auction market platform (e.g., eBay) in which a large number of buyers and sellers participate in simultaneous, single-unit auctions each period. Our model accounts for the endogenous entry of agents and the impact of intertemporal optimization on bids. Solving our model with a finite number of bidders is computationally intractable due to the curse of dimensionality, so we prove that a continuum version of our model provides a good approximation of an equilibrium in the finite model. We use the approximation to estimate the structural primitives of our model using Kindle sales on eBay. We find that just over one third of Kindle auctions on eBay result in an inefficient allocation with deadweight loss amounting to 13.5% of total possible market surplus. We also find that partial centralization - for example, running half as many 2-unit, uniform price auctions each day - would eliminate a large fraction of the inefficiency, but yield lower seller revenues. Our results highlight the importance of understanding platform composition effects - selection of agents into the market - in assessing the implications of market design.

Equilibrium in a Uniform-Price Auction with Private Values

In a model incorporating bidders with private information bidding for multiple units of a homogeneous good, I show that the equilibrium bid functions can be completely characterized, sometimes in closed form. The equilibrium bid functions can be considered aggregated bid functions from first-price single unit bidders. This property allows one to extend results from the single-unit auction literature to this multi-unit setting.

PPS: Privacy-Preserving Strategyproof Social-Efficient Spectrum Auction Mechanisms

Many spectrum auction mechanisms have been proposed for spectrum allocation problem, and unfortunately, few of them protect the bid privacy of bidders and achieve good social efficiency. In this paper, we propose PPS, a Privacy Preserving Strategyproof spectrum auction framework. We design two schemes based on PPS separately for 1) the single-unit auction model (SUA), where only single channel will be sold in the spectrum market; and 2) the multi-unit auction model (MUA), where the primary user subleases multi-unit channels to the secondary users and each of the secondary users wants to access multi-unit channels either. Since the social efficiency maximization problem is NP-hard in both auction models, we present allocation mechanisms with approximation factors of (1 + ε) and 32 separately for SUA and MUA, and further judiciously design strategyproof auction mechanisms with privacy preserving based on them. Our extensive evaluations show that our mechanisms achieve good social efficiency and with low computation and communication overhead.