Large Contests

We consider contests with many, possibly heterogeneous, players and prizes, and show that the equilibrium outcomes of such contests are approximated by the outcomes of mechanisms that implement the assortative allocation in an environment with a single agent that has a continuum of possible types. This makes it possible to easily approximate the equilibria of contests whose exact equilibrium characterization is complicated, as well as the equilibria of contests for which there is no existing equilibrium characterization.     

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.     

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.     

Weak Monotonicity Characterizes Deterministic Dominant‐Strategy Implementation

We characterize dominant‐strategy incentive compatibility with multidimensional types. A deterministic social choice function is dominant‐strategy incentive compatible if and only if it is weakly monotone (W‐Mon). The W‐Mon requirement is the following: If changing one agent's type (while keeping the types of other agents fixed) changes the outcome under the social choice function, then the resulting difference in utilities of the new and original outcomes evaluated at the new type of this agent must be no less than this difference in utilities evaluated at the original type of this agent.     

Diminishing Willingness to Pay per Quality‐Adjusted Life Year: Valuing Acute Foodborne Illness

We design and conduct a stated‐preference survey to estimate willingness to pay (WTP) to reduce foodborne risk of acute illness and to test whether WTP is proportional to the corresponding gain in expected quality‐adjusted life years (QALYs). If QALYs measure utility for health, then economic theory requires WTP to be nearly proportional to changes in both health quality and duration of illness and WTP could be estimated by multiplying the expected change in QALYs by an appropriate monetary value. WTP is elicited using double‐bounded, dichotomous‐choice questions in which respondents (randomly selected from the U.S. general adult population, n = 2,858) decide whether to purchase a more expensive food to reduce the risk of foodborne illness. Health risks vary by baseline probability of illness, reduction in probability, duration and severity of illness, and conditional probability of mortality. The expected gain in QALYs is calculated using respondent‐assessed decrements in health‐related quality of life if ill combined with the duration of illness and reduction in probability specified in the survey. We find sharply diminishing marginal WTP for severity and duration of illness prevented. Our results suggest that individuals do not have a constant rate of WTP per QALY, which implies that WTP cannot be accurately estimated by multiplying the change in QALYs by an appropriate monetary value.     

Auctions within E‐Sourcing Events

The paper presents a survey of current industry practices in designing and running auctions as part of e‐sourcing events. We report our findings from numerous interviews with auction makers in leading e‐sourcing application vendors. The differences between auction theory and auction practice pose a number of interesting and important research questions for the Operations Management community; we conclude with a discussion of lessons learned and open research questions.     

Multi‐Echelon Inventory Management under Short‐Term Take‐or‐Pay Contracts

We extend the Clark–Scarf serial multi‐echelon inventory model to include procuring production inputs under short‐term take‐or‐pay contracts at one or more stages. In each period, each such stage has the option to order/process at two different cost rates; the cheaper rate applies to units up to the contract quantity selected in the previous period. We prove that in each period and at each such stage, there are three base‐stock levels that characterize an optimal policy, two for the inventory policy and one for the contract quantity selection policy. The optimal cost function is additively separable in its state variables, leading to conquering the curse of dimensionality and the opportunity to manage the supply chain using independently acting managers. We develop conditions under which myopic policies are optimal and illustrate the results using numerical examples. We establish and use a generic one‐period result, which generalizes an important such result in the literature. Extensions to cover variants of take‐or‐pay contracts are included. Limitations are discussed.     

Generalized Reduced‐Form Auctions: A Network‐Flow Approach

We develop a network‐flow approach for characterizing interim‐allocation rules that can be implemented by ex post allocations. Our method can be used to characterize feasible interim allocations in general multi‐unit auctions where agents face capacity constraints, both ceilings and floors. Applications include a variety of settings of practical interest, ranging from individual and group‐specific capacity constraints, set‐aside sale, partnership dissolution, and government license reallocation.     

Efficient Multi‐Attribute Multi‐Unit Auctions for B2B E‐Commerce Logistics

This study is the first proposing allocatively efficient multi‐attribute auctions for the procurement of multiple items. In the B2B e‐commerce logistics problem (ELP), the e‐commerce platform is the shipper generating a large number of online orders between product sellers and buyers, and third‐party logistics (3PL) providers are carriers that can deliver these online orders. This study focuses on the ELP with multiple attributes (ELP‐MA), which is generally the problem of matching the shipper's online orders and 3PL providers given that price and other attributes are jointly evaluated. We develop a one‐sided Vickrey–Clarke–Groves (O‐VCG) auction for the ELP‐MA. The O‐VCG auction leads to incentive compatibility (on the sell side), allocative efficiency, budget balance, and individual rationality. We next introduce the concept of universally unsatisfied set to construct a primal‐dual algorithm, also called the primal‐dual Vickrey (PDV) auction. We prove that the O‐VCG auction can be viewed as a single‐attribute multi‐unit forward Vickrey (SA‐MFV) auction. Both PDV and SA‐MFV auctions realize VCG payments and truthful bidding for general valuations. This result reveals the underlying link not only between single‐attribute and multi‐attribute auctions, but between static and dynamic auctions in a multi‐attribute setting.     

Market‐Based Allocation with Indivisible Bids

We study multiunit double auctions accepting bids with indivisibility constraints. Modeling the auction problem as a Multiple Choice Knapsack Problem and using dynamic programming, we show that incremental computations during bid processing can speed the handling of key auction operations such as clearing and quoting. We propose different price‐quote policies and study their influence on the efficiency of market‐based allocation. Using a reconfigurable manufacturing scenario where agents trade large quantities of multiple goods, we demonstrate potential benefits of supporting indivisibility constraints in bidding. These benefits are highly sensitive to the form of price quote provided, indicating interesting tradeoffs in communication and allocation efficiency.     

The Affiliation Effect in First‐Price Auctions

We study the monotonicity of the equilibrium bid with respect to the number of bidders n in affiliated private‐value models of first‐price sealed‐bid auctions and prove the existence of a large class of such models in which the equilibrium bid function is not increasing in n. We moreover decompose the effect of a change in n on the bid level into a competition effect and an affiliation effect. The latter suggests to the winner of the auction that competition is less intense than she had thought before the auction. Since the affiliation effect can occur in both private‐ and common‐value models, a negative relationship between the bid level and n does not allow one to distinguish between the two models and is also not necessarily (only) due to bidders taking account of the winner's curse.     

On E‐Auctions for Procurement Operations

Electronic auctions have revolutionized procurement in the last decade. In many situations, they have replaced negotiations for supplier selection and price setting. While they have often greatly reduced transaction costs and increased competition, they have also encountered problems and resistance from suppliers resenting their intrusion on cooperative supplier/buyer relationships. In response to these issues, procurement auctions have evolved in radical new directions. Buyers use business rules to limit adverse changes. Some procurement auctions allow bidders to offer variants in the specifications of products to be supplied. Most important, some suppliers are allowing bidders to bid on packages of items, not just individual items. This tends to change procurement auctions from zero‐sum fights over supplier profit margins to win‐win searches for synergies. These changes have opened up many new research areas. Researchers are trying to improve how to deal with the computational issues involved in package auctions and to analyze the new auctions forms that are evolving. In general, equilibrium incentives are not known, and dealing with ties in package auctions is an issue. Computer scientists are analyzing the use of computerized bidding agents. Mechanisms that combine auctions with fixed buy prices or with negotiations need to be analyzed.     

Optimal Nonparametric Estimation of First‐price Auctions

This paper proposes a general approach and a computationally convenient estimation procedure for the structural analysis of auction data. Considering first‐price sealed‐bid auction models within the independent private value paradigm, we show that the underlying distribution of bidders' private values is identified from observed bids and the number of actual bidders without any parametric assumptions. Using the theory of minimax, we establish the best rate of uniform convergence at which the latent density of private values can be estimated nonparametrically from available data. We then propose a two‐step kernel‐based estimator that converges at the optimal rate.     

On the Existence of Monotone Pure‐Strategy Equilibria in Bayesian Games

We generalize Athey's (2001) and McAdams' (2003) results on the existence of monotone pure‐strategy equilibria in Bayesian games. We allow action spaces to be compact locally complete metric semilattices and type spaces to be partially ordered probability spaces. Our proof is based on contractibility rather than convexity of best‐reply sets. Several examples illustrate the scope of the result, including new applications to multi‐unit auctions with risk‐averse bidders.     

Bayesian and Dominant‐Strategy Implementation in the Independent Private‐Values Model

We prove—in the standard independent private‐values model—that the outcome, in terms of interim expected probabilities of trade and interim expected transfers, of any Bayesian mechanism can also be obtained with a dominant‐strategy mechanism.     

Non‐Manipulable House Allocation With Rent Control

In many real‐life house allocation problems, rents are bounded from above by price ceilings imposed by a government or a local administration. This is known as rent control. Because some price equilibria may be disqualified given such restrictions, this paper proposes an alternative equilibrium concept, called rationing price equilibrium, tailored to capture the specific features of housing markets with rent control. An allocation rule that always selects a rationing price equilibrium is defined, and it is demonstrated to be constrained efficient and (group) non‐manipulable for “almost all” preference profiles. In its bounding cases, the rule reduces to a number of well‐known mechanisms from the matching literature. In this sense, the housing market with rent control investigated in this paper integrates several of the predominant matching models into a more general framework.     

The 2007 Subprime Market Crisis Through the Lens of European Central Bank Auctions for Short‐Term Funds

We study European banks' demand for short‐term funds (liquidity) during the summer 2007 subprime market crisis. We use bidding data from the European Central Bank's auctions for one‐week loans, their main channel of monetary policy implementation. Our analysis provides a high‐frequency, disaggregated perspective on the 2007 crisis, which was previously studied through comparisons of collateralized and uncollateralized interbank money market rates which do not capture the heterogeneous impact of the crisis on individual banks. Through a model of bidding, we show that banks' bids reflect their cost of obtaining short‐term funds elsewhere (e.g., in the interbank market) as well as a strategic response to other bidders. The strategic response is empirically important: while a naïve interpretation of the raw bidding data may suggest that virtually all banks suffered an increase in the cost of short‐term funding, we find that, for about one third of the banks, the change in bidding behavior was simply a strategic response. We also find considerable heterogeneity in the short‐term funding costs among banks: for over one third of the bidders, funding costs increased by more than 20 basis points, and funding costs vary widely with respect to the country‐of‐origin. The funding costs we estimate using bidding data are also predictive of market‐ and accounting‐based measures of bank performance, reinforcing the usefulness of “revealed preference” information contained in bids.     

A WTP‐Choice Model: Empirical Validation,Competitive and Centralized Pricing

Willingness To Pay (WTP) of customers plays an anchoring role in pricing. This study proposes a new choice model based on WTP, incorporating sequential decision making, where the products with positive utility of purchase are considered in the order of customer preference. We compare WTP‐choice model with the commonly used (multinomial) Logit model with respect to the underlying choice process, information requirement, and independence of irrelevant alternatives. Using WTP‐choice model, we find and compare equilibrium and centrally optimal prices and profits without considering inventory availability. In addition, we compare equilibrium prices and profits in two contexts: without considering inventory availability and under lost sales. One of the interesting results with WTP‐choice model is the “loose coupling” of retailers in competition; prices are not coupled but profits are. That is, each retailer should charge the monopoly price as the collection of these prices constitute an equilibrium but each retailer's profit depends on other retailers' prices. Loose coupling fails with dependence of WTPs or dependence of preference on prices. Also, we show that competition among retailers facing dependent WTPs can cause price cycles under some conditions. We consider real‐life data on sales of yogurt, ketchup, candy melt, and tuna, and check if a version of WTP‐choice model (with uniform, triangle, or shifted exponential WTP distribution), standard or mixed Logit model fits better and predicts the sales better. These empirical tests establish that WTP‐choice model compares well and should be considered as a legitimate alternative to Logit models for studying pricing for products with low price and high frequency of purchase.     

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.     

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.