Sealed bid auctions with ambiguity: Theory and experiments

This study presents a laboratory experiment of the first and second price sealed bid auctions with independent private values, where the distribution of bidder valuations may be unknown. In our experimental setting, in first price auctions, bids are lower with the presence of ambiguity. This result is consistent with ambiguity loving in a model that allows for different ambiguity attitudes. We also find that the first price auction generates significantly higher revenue than the second price auction with and without ambiguity.     

Equilibrium reserve prices in sequential ascending auctions

We study a model where bidders have perfectly correlated valuations for two goods sold sequentially in two ascending-price auctions. The seller sets a reserve price before the beginning of each auction. Despite the lack of commitment by the seller, we characterize an equilibrium and study its properties. Strategic non-disclosure of information takes the form of non-participation in the early auction by low-valuation bidders, while high-valuation bidders bid up to their true valuations. Some buyers who would profitably buy at the reserve price refrain from participating in order to decrease the second-auction reserve price.     

The high/low divide: Self-selection by values in auction choice

Most prior theoretical and experimental work involving auction choice has assumed bidders find out their value after making a choice of which auction to enter. We examine whether or not bidders knowing their value prior to making a choice of which among multiple alternative auction formats to enter impacts their choice decision and/or the outcome of the auctions. The results show a strong impact on auction choice. Subjects with low values choose the first price sealed bid auction more often while subjects with high values choose the ascending auction more often. The number of bidders in each auction, revenue, efficiency and average bidder surplus all end up equalized.     

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.     

Multi-unit auctions with private information: an indivisible unit continuous price model

We construct a model of multi-unit auctions in which I bidders bid for two indivisible units of a common value good. Using a first-order approach, we find that there are equilibria in which bidders bid the same price for both units in the discriminatory auction, but not in the uniform auction. When there are only two bidders, under certain conditions, there are linear equilibria for both the discriminatory and the uniform auction formats. In all equilibria, bidders equalize the expected marginal benefit of bidding to the marginal costs of bidding. We show that comparison of the seller??s expected revenue across auction formats depends only on the ratio of the precision of private information to the precision of public information.     

CHARITY AUCTIONS*

In a charity auction the public‐goods nature of auction revenue affects bidding incentives. We compare equilibrium bidding and revenue in first‐price, second‐price, and all‐pay charity auctions. Bidding revenue typically varies by selling format. First‐price auctions are less lucrative than second‐price and all‐pay auctions, and with sufficiently many bidders the all‐pay auction has the highest bidding revenue. However, revenue equivalence applies when the auctioneer can set a reserve price and fees plus threaten to cancel the auction. If the auctioneer cannot threaten cancellation, a reserve and bidding fee can augment revenue but again revenue varies by auction format     

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.     

Breaking Collusion in Auctions through Speculation: An Experiment on CO2 Emission Permit Markets

The European Emission Trading Scheme (EU‐ETS) has chosen to adopt an auctioning procedure to initially allocate CO₂ emission permits. Free allocation of permits will become an exception for the third phase (2013–2020) and most firms will have to buy all their permits on the market or via auctions. The ability of bidders to collude is a key concern about the design of the auction format. To counter collusion, the auction can be open to bidders without compliance obligations (speculators). This paper aims at studying experimentally speculation as a collusion‐breaking device in two different auction mechanisms: the uniform‐price sealed‐bid auction and the ascending clock auction. Our results suggest that a uniform sealed‐bid auction open to speculators should be chosen from a revenue maximization point of view. In this mechanism, compliance agents adopt an aggressive strategy toward speculators. This strategy significantly increases the seller's revenue, compared to the more collusive clock auction. In the latter, on the contrary, bidders accommodate speculators, letting them buy permits in the auction and buying their necessary permits on the secondary market. However, as opening the auction to speculators deteriorates efficiency, the regulator faces a trade‐off between these two objectives.     

How do selling mechanisms affect profits,surplus, capacity and prices with unknown demand?

I analyze a model in which a seller wishes to sell multiple homogeneous goods to a large group of buyers with unknown demand. The seller may either sell objects via a posted‐price mechanism, a discriminatory‐price auction, a uniform‐price auction, their open‐bid analogs, or a revelation mechanism in which the seller first asks all potential buyers to report their valuations and then sets a reserve price. I show that the revelation mechanism leads to the greatest profits, the auction mechanisms result in identical expected profits and the posted‐price mechanism results in the smallest profits. However, the more profitable mechanisms impose stronger informational requirements that may make these mechanisms infeasible in practice, and the posted‐price mechanism also results in the greatest total surplus. I also find the seller chooses a lower capacity and reserve price in an auction than in the posted‐price mechanism.     

Bid Functions in Auctions and Fair Division Games: Experimental Evidence

In auctions a seller offers a commodity for sale and collects the revenue. In fair division games the object is collectively owned by the group of bidders who equally share the revenue. We run an experiment in which the participants face four types of allocation games (auctions and fair division game under two price rules, first– versus second–price rule). We collect entire bid functions rather than bids for single values and investigate price and efficiency of the different trading institutions. We find that the first–price auction is more efficient than the second–price auction, whereas economic rationality assuming heterogeneous bidders suggests the opposite. Furthermore, we study the structure of individual bid functions.     

The Relevance of a Choice of Auction Format in a Competitive Environment

We examine the relevance of an auction format in a competitive environment by comparing uniform and discriminatory price auctions with many bidders in a private values setting. We show that if the number of objects for sale is small relative to the number of bidders, then all equilibria of both auctions are approximately efficient and lead to approximately the same revenue. When the number of objects for sale is proportional to the number of bidders, then the particulars of the auction format matter. All equilibria of the uniform auction are efficient, while all of the equilibria of the discriminatory auction are inefficient. The relative revenue rankings of the auction formats can go in either direction, depending on the specifics of the environment. These conclusions regarding the efficiency and revenue ranking are in contrast to the previous literature, which focused on the case of independent information across agents.     

Allocating multiple units

Summary. This paper studies the allocation and rent distribution in multi-unit, combinatorial-bid auctions under complete information. We focus on the natural multi-unit analogue of the first-price auction, where buyers bid total payments, pay their bids, and where the seller allocates goods to maximize his revenue. While there are many equilibria in this auction, only efficient equilibria remain when the truthful equilibrium restriction of the menu-auction literature is used. Focusing on these equilibria we first show that the first-price auction just described is revenue and outcome equivalent to a Vickrey auction, which is the multi unit analogue of a second-price auction. Furthermore, we characterize these equilibria when valuations take a number of different forms: diminishing marginal valuations, increasing average valuations, and marginal valuations with single turning points. Received: December 23, 1999; revised version: December 10, 2001     

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。     

An experimental test of design alternatives for the British 3G/UMTS auction

In spring 2000, the British government auctioned off licences for Third Generation mobile telecommunications services. In the preparation of the auction, two designs involving each a hybrid of an English and a sealed-bid auction were considered by the government: A discriminatory and a uniform price variant. We report an experiment on these two designs, and also compare the results to those with a pure English auction. Both hybrids are similar in efficiency, revenue differences disappear as bidders get experienced. Compared to the discriminatory format, the pure English auction induces more entry.     

Bidding behavior in competing auctions: Evidence from eBay

Much of the existing auction literature treats auctions as running independently of one another, with each bidder choosing to participate in only one auction. However, in many online auctions, a number of substitutable goods are auctioned concurrently and bidders can bid on several auctions at the same time. Recent theoretical research shows how bidders can gain from the existence of competing auctions, the current paper providing the first empirical evidence in support of competing auctions theory using online auctions data from eBay. Our results indicate that a significant proportion of bidders do bid across competing auctions and that bidders tend to submit bids on auctions with the lowest standing bid, as the theory predicts. The paper also shows that winning bidders who cross-bid pay lower prices on average than winning bidders who do not.     

Multiple unit auctions with strategic price-quantity decisions

Summary. I study a multiple unit auction where symmetric risk-neutral bidders choose prices and quantities endogenously. In the model, bidders (a) may place non-linear valuations on the auctioned units, and (b) bid for several units at the same price (“lumpy” bids). I characterize quantity-symmetric and strictly monotone-increasing price equilibria for discriminatory and competitive auctions, and show that (i) if quantity strategy profiles are equal across auctions revenue- equivalence holds, (ii) expected revenue is higher if bidders bid for the entire supply rather than for shares of it, and (iii) equilibrium allocations may fail to be Pareto-optimal. Received: April 14, 1995; revised version: September 3, 1997     

Revenue ranking of first-price auctions with resale

When the price setter in post-auction resale is chosen according to exogenous probabilities, Hafalir and Krishna (2008) [2] showed that the first-price auction brings more expected revenues than the second-price auction with truth-bidding bidders. We complete their revenue ranking by proving that the first-price auction produces higher expected revenues the higher the probability the auction winner sets the resale price.     

Multiple-unit English auctions

This paper examines the outcome of an ascending-price multiple-unit auction. Two bidders, facing continuous, downward-sloping demand functions, participate in the auction of some divisible objects. The auctioneer starts the process by announcing an initial price and asking both bidders to submit sealed-bids of desired quantities. The auctioneer increases the price until the total amount bid for is less than the total supply. We compute the outcome of this auction game under full information and suggest that this mechanism may not maximize expected revenue.     

Rational Buyer Meets Rational Seller: Reserves Market Equilibria under Alternative Auction Designs

We examine efficiency properties and incentive compatibility of alternative auction formats that an electricity network system operator may use for the procurement of ancillary services required for real-time operations. We model the procurement auction as a hierarchical multiproduct auction, and study several designs such as a uniform price auction minimizing revealed social cost, a uniform price auction minimizing the system operator's cost and a pay as bid auction minimizing revealed social cost. We take into account that rational bidders will respond to any market design so as to maximize their expected benefit from participating in that market. Under the assumptions of our model, we show that the uniform price auction minimizing revealed social cost is the only one that guarantees productive efficiency. We also find that expected revenue (payment in our case) equivalence between pay as bid and uniform price auctions does not extend to the hierarchical products case and the ranking of these auctions is ambiguous and depends on the data. For the procurement auction minimizing the system operator's cost, we show that misrepresentation of capability may result in capacity shortages if there are capacity constraints. For the case where only higher capability resources are constrained, this will result in random price spikes decreasing in frequency with the price cap (this is the amount paid to capacity in demand states with shortages). When lower type resources are capacity constrained as well, price spikes will be seen for both type of resources. Such artificial shortages result in reduced reliability in real-time operations.     

Reserve Prices without Commitment

When potential bidders in an auction have to incur a cost to prepare their bids and thus to learn their valuations, imposing a reserve price and announcing that in case no bid is submitted there will be another auction without a reserve price is both revenue and welfare improving. Reserve prices that induce less than maximum entry in the first auction may be optimal. Also, entry fees are not necessarily better instruments than reserve prices.Journal of Economic LiteratureClassification Number: D44.