Auctions with variable supply: Uniform price versus discriminatory

We examine an auction in which the seller determines the supply after observing the bids. We compare the uniform price and the discriminatory auction in a setting of supply uncertainty, where uncertainty is caused by the interplay of two factors: the seller's private information about marginal cost and the seller's incentive to sell the profit-maximizing quantity, given the received bids. In every symmetric mixed strategy equilibrium, bidders submit higher bids in the uniform price auction than in the discriminatory auction. In the two-bidder case, this result extends to the set of rationalizable strategies. As a consequence, we find that the uniform price auction generates a higher expected revenue for the seller and a higher trade volume.     

Side-communication yields efficiency of ascending auctions: The two-items case

We analyze a simultaneous ascending auction with anonymous item prices, for two items that are substitutes. This popular format entails increased opportunities for coordination among bidders, since bids are observable and can be used as signaling. This has happened, e.g., in the Netherlands 3G Telecom Auction and in the FCC auctions.While it may seem that such bidding harms economic efficiency, we show that side communication may actually improve efficiency: We describe an ex-post subgame-perfect equilibrium, with limited communication, that is ex-post efficient. In contrast, without communication, we show that there is no ex-post equilibrium which is ex-post efficient in this auction.In this equilibrium, bidders initially report true demands, and then perform a single demand reduction at a certain point, determined using a single message exchanged between the bidders. This limited signaling opportunity resolves the strategic problems of myopic bidding, and may improve the social welfare.     

Profit Maximizing in Auctions of Public Goods

A profit-maximizing auctioneer can provide a public good to a group of agents. Each group member has a private value for the good being provided to the group. We investigate an auction mechanism where the auctioneer provides the good to the group only if the sum of their bids exceeds a reserve price declared previously by the auctioneer. For the two-bidder case with private values drawn from a uniform distribution we characterize the continuously differentiable symmetric equilibrium bidding functions for the agents, and we find the optimal reserve price for the auctioneer when such functions are used by the bidders. We also examine another interesting family of equilibrium bidding functions for this case, with a discrete number of possible bids, and show the relation (in the limit) to the differentiable bidding functions.     

A Uniform Price Auction for Conservation Easements in the Canadian Prairies

This paper describes the application of a uniform price auction with a hidden reserve price in a field project aimed at discovering Canadian landowners’ willingness to accept compensation for placing conservation easements on their lands. This is the only project of this kind in Canada to date, and one of the few worldwide. The paper discusses the design of the auction, describes its implementation, and presents its results. The bids received in the auction conformed with known factors affecting opportunity costs and willingness to accept. The information from this auction was successful in guiding a long-term easement procurement program.     

Explaining Overbidding in First Price Auctions Using Controlled Lotteries

In this paper, we study the behavior of individuals when facing two different, but incentive-wise identical, institutions. We pair the first price auction with an equivalent lottery. Once a subject is assigned a value for the auctioned object, the first price auction can be modeled as a lottery in which the individual faces a given probability of winning a certain payoff. This set up allows us to explore to what extent the misperception of the probability of winning in the auction is responsible for bidders in a first price auction to bidding above the risk neutral Nash equilibrium prediction. The first result we obtain is that individuals, even though facing the same choice over probability/payoff pairs, behave differently depending on the type of choice they are called to make. When facing an auction, subjects with high values tend to bid significantly above the bid they choose in the corresponding lottery environment. We further find that in both the lottery and the auction environments, subjects tend to bid in excess of the bid predicted by the risk neutral model, at least for intermediate range values. Finally, we find that the difference between the lottery behavior and the auction behavior is substantially, but not totally, eliminated by showing the subjects the probability of winning the auction.     

Sequential vs. single-round uniform-price auctions

We study sequential and single-round uniform-price auctions with affiliated values. We derive symmetric equilibrium for the auction in which k₁ objects are sold in the first round and k₂ in the second round, with and without revelation of the first-round winning bids. We demonstrate that auctioning objects in sequence generates a lowballing effect that reduces the first-round price. Total revenue is greater in a single-round, uniform auction for k=k₁+k₂ objects than in a sequential uniform auction with no bid announcement. When the first-round winning bids are announced, we also identify a positive informational effect on the second-round price. Total expected revenue in a sequential uniform auction with winning-bids announcement may be greater or smaller than in a single-round uniform auction, depending on the model's parameters.     

Second chance offers in auctions

This paper examines situations in which a seller might make a second chance (take-it-or-leave-it) offer to a non-winning bidder at a price equal to their bid at auction. This study is motivated by the take-it-or-leave-it second chance offer rules used by eBay and a number of state procurement agencies. Equilibrium bidder behavior is determined for IPV sealed bid first price, second price, English, and Vickrey auctions when a second chance offer will be made with an exogenous probability $p$ . In all but the Vickrey auction (which elicits the dominant strategy of bidding one’s value) equilibrium bids are lower than if there were no possibility of a second chance offer and higher than if a second chance offer will be made for certain. Further, the possibility of a second chance offer erodes the strategic equivalence between second price bids and English auction drop out levels. If bidders are risk averse (with CRRA preferences), this difference leads to expected revenue dominance of the second price over the English auction, both of which dominate the Vickrey auction. The first price auction is also shown to revenue dominate the Vickrey auction, and moreover, numerical results and intuition from existing literature suggest that the first price auction revenue dominates the second price auction.     

Commitment in sequential auctioning: advance listings and threshold prices

This paper models sequential auctioning of two perfect substitutes by a strategic seller, who learns about demand from the first-auction price. The seller holds the second auction only when the remaining demand is strong enough to cover her opportunity cost. Bidding in anticipation of such a contingent future auction is characterized, including a sufficient condition for existence of an invertible (increasing symmetric pure-strategy) bidding equilibrium that facilitates the seller’s learning. A unique invertible bidding equilibrium exists for the Dutch auction format, but only when the second auction is sufficiently discounted by the bidders. In the equilibrium, high-valuation bidders shade their bids down as if the second auction were guaranteed. To counter such strategic bidding, the seller would value ex-ante commitment to hold the second auction less often. Three forms of such commitment are analyzed: commitment to list future auctions in advance, commitment to not hold the second auction unless the first price exceeds a publicly announced threshold, and commitment to a reserve-price in the second auction. I would like to thank Georgios Katsenos, Thomas Jeitschko, Miguel Villas-Boas, George Deltas, and an anonymous referee for thorough and insightful feedback.     

AUCTION–LOTTERY HYBRID MECHANISMS: STRUCTURAL MODEL AND EMPIRICAL ANALYSIS

This article studies an auction–lottery hybrid mechanism that is widely adopted in allocating new vehicle licenses in China. We characterize individuals' entry and bidding strategies in a symmetric Bayesian Nash equilibrium, structurally estimate individuals' value distribution from a data set of a Guangzhou program, and evaluate the performance of the mechanism. Based on the estimated distribution and counterfactual analysis, our study suggests that a hybrid mechanism preserves 83% efficiency and 52% of revenue, while it improves equity by 25 times compared to a pure auction. We show that allowing auction losers to participate in the lottery can further enhance the performance.     

Auctions in which losers set the price

We study auctions of a single asset among symmetric bidders with affiliated values. We show that the second-price auction minimizes revenue among all efficient auction mechanisms in which only the winner pays, and the price only depends on the losers' bids. In particular, we show that the kth price auction generates higher revenue than the second-price auction, for all k>2. If rationing is allowed, with shares of the asset rationed among the t highest bidders, then the (t+1)st price auction yields the lowest revenue among all auctions with rationing in which only the winners pay and the unit price only depends on the losers' bids. Finally, we compute bidding functions and revenue of the kth price auction, with and without rationing, for an illustrative example much used in the experimental literature to study first-price, second-price and English auctions.     

A choice of auction format in seller cheating: a signaling game analysis

In this paper, we examine which auction format, first-price or second-price, a seller will choose when he can profitably cheat in a second price auction by observing all bids by possible buyers and submitting a shill bid as pretending to be a buyer. We model this choice of auction format in seller cheating as a signaling game in which the buyers may regard the selection of a second price auction by the seller as a signal that he is a shill bidder. By introducing trembling-hand perfectness as a refinement of signaling equilibrium, we find two possible strictly perfect signaling equilibria. One is a separating equilibrium in which a noncheating honest seller selects a first price auction and a cheating seller does a second price auction. In another pooling equilibrium, however, both cheating and non-cheating sellers select a second price auction. The conclusion that a seller chooses a second price auction even if he cannot cheat is in contrast to the previous literature, which focused on the case of independent values. We thank an anonymous referee for useful comments that have improved the paper. This research was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (B) 15310023 and (C) 18530139.     

Bidding ‘as if’ risk neutral in experimental first price auctions without information feedback

Experimental research on first price sealed bid auctions has usually involved repeated settings with information feedback on winning bids and payoffs after each auction round. Relative to the risk neutral Nash equilibrium, significantly higher bidding has been reported. The present paper reports the results of experimental first price auctions with n=7 where feedback on payoffs and winning bids is withheld. Under these conditions, average bidding is below the risk neutral Nash equilibrium prediction but converges to it with repetition.

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Asymmetric Nash equilibrium in emission rights auctions

This paper studies the problems of emission rights auctions, and presents a uniform price auction mechanism based on three assumptions, i.e., all buyers are asymmetric, every buyer submits a nonincreasing continuous demand function, and every buyer's valuation to per unit of the emission rights is common value information. It focuses on solving the asymmetric Nash equilibrium for this auction mechanism. It concludes that there exist multiple Nash equilibria in our auction mechanism, but the arbitrary low equilibrium prices cannot emerge. We also give several suggestions on how to induce the auction to a desired ideal equilibrium state in mechanism design of emission rights auctions.     

Lottery or waiting-line auction?

This paper studies the efficiencies of the two most widely used non-price allocation mechanisms: lotteries and waiting-line auctions. As our analysis suggests, in addition to the fairness of the mechanism, the use of lotteries in lieu of waiting-line auctions can be also justified from an efficiency point of view. In particular, we show that the less dispersed consumers’ time valuations are, the more efficient is a lottery relative to a waiting-line auction. In addition, we identify four conditions under which a lottery dominates a waiting-line auction in expected social surplus preserving. Furthermore, the numerical simulations we conduct indicate that over a predominantly wide range of circumstances, a lottery is more socially efficient than a waiting-line auction as an allocative mechanism in the absence of a conventional price system.     

向上叫价时钟双向拍卖机制设计

通过深入分析统一价格密封双向拍卖机制的诸多缺陷，充分借鉴单向拍卖市场上时钟拍卖的基本思想，将时钟拍卖引入双向拍卖市场，构建了一个无论从分配效率方面考虑还是从竞价风险方面考虑都优于统一价格密封双向拍卖机制，不仅为同类物品确定统一价格，还可以为不同类的物品确定其不同的价格的向上叫价时钟双向拍卖机制。     

Vertical Product Differentiation When Quality is Scarce: The Case of n > 2 Firms

This paper describes a model of vertical product differentiation in which more than two firms compete in quality and price. Quality is of fixed supply, so firms participate in an auction to attain it. Firms then simultaneously choose prices. The paper determines equilibrium bids in the quality auction and the Bertrand equilibrium prices. In equilibrium one firm attains all the units of quality, but pays a price such that it, like the minimum-quality firms, earns zero profits. Aggregate welfare is computed, and is shown to decrease as competition increases.     

DEMAND REDUCTION IN MULTI‐UNIT AUCTIONS WITH VARYING NUMBERS OF BIDDERS: THEORY AND EVIDENCE FROM A FIELD EXPERIMENT*

Recent auction theory and experimental results document strategic demand reduction by bidders in uniform‐price auctions. The present article extends this area of research to consider the effects of varying the number of bidders. Our theoretical model predicts that demand reduction should decrease with an increase in the number of bidders. Considerable demand reduction remains even in the asymptotic limit, although truthful bidding yields profits very close to those of equilibrium play. We experimentally confirm several of our predictions by examining bidding behavior of subjects in an actual marketplace, auctioning dozens of sportscards using both uniform‐price and Vickrey auction formats.     

Entry decisions and bidding behavior in sequential first-price procurement auctions: An experimental study

Though many real life auctions are run independently of each other, from the bidders' point of view they often form sequences of auctions. We investigate how behavior responds to the additional incentives that are present in such auction sequences. Comparing subjects' decisions in single first-price procurement auctions with their decisions in a game consisting of two subsequent first-price procurement auctions, we find that, in line with the theoretical prediction, entry and bidding behavior is crucially affected by the opportunity cost of early bid submission. Though, entry decisions and average bids in the auction sequence systematically deviate from the perfect Bayesian equilibrium prediction. While the nature of the opponent (human being or computer) has no significant effect on these findings, giving subjects additional feedback on winners and prices seems to reduce the deviations from the equilibrium prediction.     

Individual behavior of first-price auctions: The importance of information feedback in computerized experimental markets

This article reports the results of an individual choice experiment designed to test the Nash equilibrium predictions of the first-price sealed-bid auction. A subject faced in 100 auctions always the same resale value and competed with computer-simulated bids. The design used between-subjects variation and involved information feedback as the treatment variable. Earlier experimental work on first price auctions has frequently reported an overbidding relative to the risk neutral Nash equilibrium. Our data provide evidence that overbidding can be fostered by the standard information feedback in auction experiments, which, after each auction, reveals the winning bid only. By means of learning direction theory we explain the individual bidding dynamics in our experiment. Finally we apply impulse balance theory and make long run predictions of individual bidding behavior.     

Lottery versus all-pay auction contests: A revenue dominance theorem

We allow a contest organizer to bias a contest in a discriminatory way; i.e., she can favor specific contestants by designing the contest rule in order to maximize total equilibrium effort (resp. revenue). The two predominant contest regimes are considered, all-pay auctions and lottery contests. For all-pay auctions the optimal bias is derived in closed form: It implies extreme competitive pressure among active contestants and low endogenous participation rates. Moreover, the exclusion principle advanced by Baye et al. (1993) becomes obsolete in this case. In contrast, the optimally biased lottery induces a higher number of actively participating contestants due to softer competition. Our main result regarding total revenue comparison under the optimal biases reveals that the all-pay auction revenue-dominates the lottery contest for all levels of heterogeneity among contestants. The incentive effect due to a strongly discriminating contest rule (all-pay auction) dominates the participation effect due to a weakly discriminating contest rule (lottery).