Introduction to the Special Issue on E‐Auctions for Procurement Operations

We present nine papers on e‐auctions for procurement operations. The first of the issue's three sections is a foreword highlighting current trends and future research directions. The second section is composed of three commissioned survey papers, covering auctions within e‐sourcing events, electronic markets for truckload transportation, and games and mechanism design in machine scheduling. The final section consists of five research papers on the following topics: whether auction parameters affect buyer surplus in e‐auctions for procurement, collusion in second‐price auctions under minimax regret, the effect of timing on jump bidding in ascending auctions, market‐based allocation with indivisible bids, and ranked items auctions and online advertisement.     

First‐Price Auctions With General Information Structures: Implications for Bidding and Revenue

We explore the impact of private information in sealed‐bid first‐price auctions. For a given symmetric and arbitrarily correlated prior distribution over values, we characterize the lowest winning‐bid distribution that can arise across all information structures and equilibria. The information and equilibrium attaining this minimum leave bidders indifferent between their equilibrium bids and all higher bids. Our results provide lower bounds for bids and revenue with asymmetric distributions over values. We also report further characterizations of revenue and bidder surplus including upper bounds on revenue. Our work has implications for the identification of value distributions from data on winning bids and for the informationally robust comparison of alternative auction mechanisms.     

付费搜索拍卖建模与两类排名机制比较研究

在综合付费搜索拍卖静态博弈研究成果的基础上,通过归纳广告主估价函数结构和梳理拍卖规则,建立了较为一般性的付费搜索拍卖模型,定义了GSP机制下付费搜索拍卖的纳什均衡条件和无嫉妒均衡条件并阐述了二者之间的关系,证明了有效竞价排名相对于单纯竞价排名具有更好的均衡配置效率,但是不能保证搜索引擎收益一定得到提高,最后通过数值分析进一步指出,只有广告主相关度因子存在较大差别时,有效竞价排名相对于单纯竞价排名的优势才能得以体现。     

Keyword Auctions,Unit‐Price Contracts,and the Role of Commitment

Motivated by the enormous growth of keyword advertising, this paper explores the design of performance‐based unit‐price contract auctions, in which bidders bid their unit prices and the winner is chosen based on both their bids and performance levels. The previous literature on unit‐price contract auctions usually considers a static case where bidders' performance levels are fixed. This paper studies a dynamic setting in which bidders with a low performance level can improve their performance at a certain cost. We examine the effect of the performance‐based allocation on overall bidder performance, auction efficiency, and the auctioneer's revenue, and derive the revenue‐maximizing and efficient policies accordingly. Moreover, the possible upgrade in bidders' performance level gives the auctioneer an incentive to modify the auction rules over time, as is confirmed by the practice of Yahoo! and Google. We thus compare the auctioneer's revenue‐maximizing policies when she is fully committed to the auction rule and when she is not, and show that the auctioneer should give less preferential treatment to low‐performance bidders when she is fully committed.     

Reverse Auctions with Multiple Reinforcement Learning Agents*

Reverse auctions in business‐to‐business (B2B) exchanges provide numerous benefits to participants. Arguably the most notable benefit is that of lowered prices driven by increased competition in such auctions. The competition between sellers in reverse auctions has been analyzed using a game‐theoretic framework and equilibria have been established for several scenarios. One finding of note is that, in a setting in which sellers can meet total demand with the highest‐bidding seller being able to sell only a fraction of the total capacity, the sellers resort to a mixed‐strategy equilibrium. Although price randomization in industrial bidding is an accepted norm, one might argue that in reality managers do not utilize advanced game theory calculations in placing bids. More likely, managers adopt simple learning strategies. In this situation, it remains an open question as to whether the bid prices converge to the theoretical equilibrium over time. To address this question, we model reverse‐auction bidding behavior by artificial agents as both two‐player and n‐player games in a simulation environment. The agents begin the game with a minimal understanding of the environment but over time analyze wins and losses for use in determining future bids. To test for convergence, the agents explore the price space and exploit prices where profits are higher, given varying cost and capacity scenarios. In the two‐player case, the agents do indeed converge toward the theoretical equilibrium. The n‐player case provides results that reinforce our understanding of the theoretical equilibria. These results are promising enough to further consider the use of artificial learning mechanisms in reverse auctions and other electronic market transactions, especially as more sophisticated mechanisms are developed to tackle real‐life complexities. We also develop the analytical results when one agent does not behave strategically while the other agent does and show that our simulations for this environment also result in convergence toward the theoretical equilibrium. Because the nature of the best response in the new setting is very different (pure strategy as opposed to mixed), it indicates the robustness of the devised algorithm. The use of artificial agents can also overcome the limitations in rationality demonstrated by human managers. The results thus have interesting implications for designing artificial agents in automating bid responses for large numbers of bids where human intervention might not always be possible.     

On the Existence of Pure Strategy Monotone Equilibria in Asymmetric First‐Price Auctions

We establish the existence of pure strategy equilibria in monotone bidding functions in first‐price auctions with asymmetric bidders, interdependent values, and affiliated one‐dimensional signals. By extending a monotonicity result due to Milgrom and Weber (1982), we show that single crossing can fail only when ties occur at winning bids or when bids are individually irrational. We avoid these problems by considering limits of ever finer finite bid sets such that no two bidders have a common serious bid, and by recalling that single crossing is needed only at individually rational bids. Two examples suggest that our results cannot be extended to multidimensional signals or to second‐price auctions.     

Speculation in Standard Auctions with Resale

In standard auctions resale creates a role for a speculator—a bidder who is commonly known to have no use value for the good on sale. We study this issue in environments with symmetric independent private‐value bidders. For second‐price and English auctions the efficient value‐bidding equilibrium coexists with a continuum of inefficient equilibria in which the speculator wins the auction and makes positive profits. First‐price and Dutch auctions have an essentially unique equilibrium, and whether or not the speculator wins the auction and distorts the final allocation depends on the number of bidders, the value distribution, and the discount factor. Speculators do not make profits in first‐price or Dutch auctions.     

Do Auction Parameters Affect Buyer Surplus in E‐Auctions for Procurement?

Although the initial euphoria about Internet‐enabled reverse auctions has given way to a cautious but widespread use of reverse auctions in business‐to‐business (B2B) procurement, there is a limited understanding of the effect of auction design parameters on buyer surplus. In this paper, we study the effect of bidding competition, information asymmetry, reserve price, bid decrement, auction duration, and bidder type on buyer surplus. We collected field data on more than 700 online procurement auctions conducted by a leading auctioneer and involving procurement items worth millions of dollars. Consistent with the predictions of auction theory, the results indicate that bidding competition, reserve price, and information sharing affect buyer surplus. Unlike previous findings in the consumer‐to‐consumer context, we find that bid decrement and auction duration have no effect in B2B procurement auctions. Our results suggest that use of the rank‐bidding format increases buyer surplus when incumbent suppliers participate in the auction. We discuss the theoretical and managerial implications of these findings for future research and for optimal design of online procurement auctions.     

Transparency in Buyer‐Determined Auctions: Should Quality be Private or Public?

We study buyer‐determined procurement auctions where both price and non‐price characteristics of bidders matter for being awarded a contract. Although, in scoring auctions bidders perfectly know how price and non‐price attributes determine the awarding of the contract, this remains uncertain in buyer‐determined auctions where the buyer is free to choose once all bids have been submitted. We analyze the impact of information bidders have with respect to the buyer's awarding decision. As we show theoretically whether it is in the buyer's interest to conceal the impact of non‐price characteristics depends on how important the quality aspects of the procured good are to the buyer: The more important quality aspects are, the more interesting concealment becomes. In a counterfactual analysis using data from a large European procurement platform, we analyze the reduction of non‐price information available to the bidders. Confirming our hypothesis, for auction categories where bidders’ non‐price characteristics strongly influence buyers’ decisions concealment of non‐price information leads to an increase in buyers’ surplus of up to 15% due to higher competitive pressure and lower bids. Conversely, for categories where bidders’ non‐price characteristics are of little importance concealment of non‐price information leads to a decrease in buyers’ surplus of up to 6%.     

Level‐k Auctions: Can a Nonequilibrium Model of Strategic Thinking Explain the Winner's Curse and Overbidding in Private‐Value Auctions?

This paper proposes a structural nonequilibrium model of initial responses to incomplete‐information games based on “level‐k” thinking, which describes behavior in many experiments with complete‐information games. We derive the model's implications in first‐ and second‐price auctions with general information structures, compare them to equilibrium and Eyster and Rabin's (2005) “cursed equilibrium,” and evaluate the model's potential to explain nonequilibrium bidding in auction experiments. The level‐k model generalizes many insights from equilibrium auction theory. It allows a unified explanation of the winner's curse in common‐value auctions and overbidding in those independent‐private‐value auctions without the uniform value distributions used in most experiments.     

Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information

This paper analyzes a class of games of incomplete information where each agent has private information about her own type, and the types are drawn from an atomless joint probability distribution. The main result establishes existence of pure strategy Nash equilibria (PSNE) under a condition we call the single crossing condition (SCC), roughly described as follows: whenever each opponent uses a nondecreasing strategy (in the sense that higher types choose higher actions), a player's best response strategy is also nondecreasing. When the SCC holds, a PSNE exists in every finite‐action game. Further, for games with continuous payoffs and a continuum of actions, there exists a sequence of PSNE to finite‐action games that converges to a PSNE of the continuum‐action game. These convergence and existence results also extend to some classes of games with discontinuous payoffs, such as first‐price auctions, where bidders may be heterogeneous and reserve prices are permitted. Finally, the paper characterizes the SCC based on properties of utility functions and probability distributions over types. Applications include first‐price, multi‐unit, and all‐pay auctions; pricing games with incomplete information about costs; and noisy signaling games.     

Market Good Flexibility in Capacity Auctions

We consider the allocation of limited production capacity among several competing agents through auctions. Our focus is on the contribution of flexibility in market good design to effective capacity allocation. The application studied is a capacity allocation problem involving several agents, each with a job, and a facility owner. Each agent generates revenue by purchasing capacity and scheduling its job at the facility. Ascending auctions with various market good designs are compared. We introduce a new market good that provides greater flexibility than those previously considered in the literature. We allow ask prices to depend both on agents’ utility functions and on the number of bids at the previous round of the auction, in order to model and resolve resource conflicts. We develop both optimal and heuristic solution procedures for the winner determination problem. Our computational study shows that flexibility in market good design typically increases system value within auctions. A further increase is achieved if each agent is allowed to bid for multiple market goods at each round. On average, the multiple flexible market goods auction provides over 95% of the system value found by centralized planning.     

Behavior in Multi‐Unit Demand Auctions: Experiments with Uniform Price and Dynamic Vickrey Auctions

We experimentally investigate the sensitivity of bidders demanding multiple units of a homogeneous commodity to the demand reduction incentives inherent in uniform price auctions. There is substantial demand reduction in both sealed bid and ascending price clock auctions with feedback regarding rivals' drop‐out prices. Although both auctions have the same normal form representation, bidding is much closer to equilibrium in the ascending price auctions. We explore the behavioral process underlying these differences along with dynamic Vickrey auctions designed to eliminate the inefficiencies resulting from demand reduction in the uniform price auctions.     

The Effect of Timing on Jump Bidding in Ascending Auctions

We investigate the role of timing in ascending auctions under the premise that time is a valuable resource. Traditional models of the English auction ignore timing issues by assuming that the auction occurs instantaneously. However, when auctions are slow, as Internet auctions used for procurement often are, there are significant opportunity or monitoring costs to bidders, and the choice of the size of the jump bid becomes a strategic decision. We study the choice in the experimental laboratory by systematically varying the opportunity costs associated with fast bidding. When time is more valuable bidders respond by choosing larger jump bids. Surprisingly, the economic performance of the auction is not significantly affected. We develop a simple model of ascending auctions with impatient bidders that provides insights into the effect jump bids have on auction performance.     

An Analysis of Scoring and Buyer‐Determined Procurement Auctions

In procurement auctions, the object for sale is a contract, bidders are suppliers, and the bid taker is a buyer. The suppliers bidding for the contract are usually the current supplier (the incumbent) and a group of potential new suppliers (the entrants). As the buyer has an ongoing relationship with the incumbent, he needs to adjust the bids of the entrants to include non‐price attributes, such as the switching costs. The buyer can run a scoring auction, in which suppliers compete on the adjusted bids or scores, or, he can run a buyer‐determined auction, in which suppliers compete on the price, and the buyer adjusts a certain number of the bids with the non‐price attributes after the auction to determine the winner. Unless the incumbent has a significant cost advantage over the entrants, I find that the scoring auction yields a lower average cost for the buyer, if the non‐price attributes are available. If the non‐price attributes are difficult or expensive to obtain, the buyer could run a buyer‐determined auction adjusting only the lowest price bid.     

A Mechanism Design Approach to Ranking Asymmetric Auctions

I propose a new mechanism design approach to the problem of ranking standard auctions with two heterogeneous bidders. A key feature of the approach is that it may be possible to rank two auctions even if neither dominates the other for all combinations of types. The approach simplifies the analysis and unifies results in the existing literature. Roughly speaking, the first‐price auction is more profitable than the second‐price auction when the strong bidder's distribution is flatter and more disperse than the weak bidder's distribution. Applications include auctions with one‐sided externalities. Moreover, contrary to previous work, reserve prices are easily handled. Finally, the method can be extended to some environments with many bidders.     

Existence of Equilibrium in Single and Double Private Value Auctions1

We show existence of equilibria in distributional strategies for a wide class of private value auctions, including the first general existence result for double auctions. The set of equilibria is invariant to the tie‐breaking rule. The model incorporates multiple unit demands, all standard pricing rules, reserve prices, entry costs, and stochastic demand and supply. Valuations can be correlated and asymmetrically distributed. For double auctions, we show further that at least one equilibrium involves a positive volume of trade. The existence proof establishes new connections among existence techniques for discontinuous Bayesian games.     

Common Value Auctions with Insider Information

Bidding is studied in first-price common value auctions where an insider is better informed than other bidders (outsiders) about the value of the item. With inexperienced bidders, having an insider does not materially reduce the severity of the winner's curse compared to auctions with a symmetric information structure (SIS). In contrast, super-experienced bidders, who have largely overcome the winner's curse, satisfy the comparative static predictions of equilibrium bidding theory: (i) average seller's revenue is larger with an insider than in SIS auctions, (ii) insiders make substantially greater profits, conditional on winning, than outsiders, and (iii) insiders increase their bids in response to more rivals. Further, changes in insiders' bids are consistent with directional learning theory (Selten and Buchta (1994)).     

Ranked Items Auctions and Online Advertisement

We study auctions for a set of commonly‐ranked items where each buyer has unit demand. This setting has promising applications in areas such as keyword auctions in the search engine advertising industry, the sale of quality‐ranked raw materials, etc. An auction mechanism suitable for this setting is the simultaneous pooled auction (SPA), where each bidder simultaneously submits a single bid and is allocated an object based on the rank of his bid among all the bids. We study how to improve the seller's expected revenue by enforcing a reserve price in an SPA. We find that the use of an appropriate reserve price may significantly increase the seller's revenue, especially when the number of items for sale is relatively large compared to the number of participating bidders. One inherent problem in the SPA is that some bidders may incur ex post losses; that is, they pay more than what they value the received objects. We propose a tailored VCG mechanism that generates the same expected revenue as the SPA does, while bidders do not incur any ex post loss. We also discuss the potential applications of this research to keyword auctions.     

All‐Pay Contests

This paper studies a class of games, “all‐pay contests,” which capture general asymmetries and sunk investments inherent in scenarios such as lobbying, competition for market power, labor‐market tournaments, and R&D races. Players compete for one of several identical prizes by choosing a score. Conditional on winning or losing, it is weakly better to do so with a lower score. This formulation allows for differing production technologies, costs of capital, prior investments, attitudes toward risk, and conditional and unconditional investments, among others. I provide a closed‐form formula for players' equilibrium payoffs and analyze player participation. A special case of contests is multiprize, complete‐information all‐pay auctions.