Beyond chopsticks: Symmetric equilibria in majority auction games

Majority auction games are simultaneous sealed-bid auctions of identical objects among identical bidders who each want to win a specified fraction (more than a half) of the objects. Each bidder receives no benefit from winning less than the specified fraction and no additional benefit from winning more than it. Symmetric equilibria having simple, intuitive forms are shown to exist in first-price, second-price and all-pay versions of such games when the number of bidders is sufficiently large. This contrasts with earlier results for the two-bidder “pure chopstick” majority auction games where the only known equilibria are more complicated.     

Auctions with Price-Proportional Benefits to Bidders

After some auctions, including Amish estate sales and buyer rings′ knockout auctions, each bidder receives a share of the revenue generated by the auction. We show that in the symmetric case, equilibrium bids in both first-price sealed-bid auctions and oral auctions increase as each bidder′s share increases. In the case of independent signals, oral auctions result in higher expected equilibrium prices than do first-price sealed-bid auctions. Journal of Economic, Literature classification number: D44.     

Expected revenue of all-pay auctions and first-price sealed-bid auctions with budget constraints

We show that all-pay auctions dominate first-price sealed-bid auctions when bidders face budget constraints. This ranking is explained by the fact that budget constraints bind less frequently in the all-pay auctions, which leads to more aggressive bidding in that format.     

Regret in auctions: theory and evidence

The sealed-bid first-price auction of a single object in the case of independent privately-known values is the simplest auction setting and understanding it is important for understanding more complex mechanisms. But bidders bid above the risk-neutral Nash equilibrium theory prediction. The reasons for this “over bidding” remain an unsolved puzzle. Several explanations have been offered, including risk aversion, social comparisons, and learning. We present a new explanation based on regret and a model that explains not only the observed over bidding in sealed-bid first-price auctions, but also behavior in several other settings that is inconsistent with risk aversion. The authors gratefully acknowledge support from the National Science Foundation.     

Information acquisition during a descending auction

We compare the effects of information acquisition during a descending auction with its static counterpart, the first-price sealed-bid auction. In a framework with heterogeneous prior information, we show that an equilibrium with information acquisition exists in both auction formats. We show that everything else equal information acquisition is more desirable in the dynamic auction. Moreover, we characterize a set of parameter values where more information is acquired in the dynamic auction in equilibrium. If the costs of information acquisition are sufficiently low, the sealed-bid auction generates more revenue although the descending auction is more efficient.     

On the continuous equilibria of affiliated-value,all-pay auctions with private budget constraints

We consider all-pay auctions in the presence of interdependent, affiliated valuations and private budget constraints. For the sealed-bid, all-pay auction we characterize a symmetric equilibrium in continuous strategies for the case of N bidders. Budget constraints encourage more aggressive bidding among participants with large endowments and intermediate valuations. We extend our results to the war of attrition where we show that budget constraints lead to a uniform amplification of equilibrium bids among bidders with sufficient endowments. An example shows that with both interdependent valuations and private budget constraints, a revenue ranking between the two auction formats is generally not possible. Equilibria with discontinuous bidding strategies are discussed.     

Pre-auction offers in asymmetric first-price and second-price auctions

We consider first-price and second-price auctions with asymmetric buyers, and examine whether pre-auction offers to a subset of buyers are profitable. A single offer is never profitable prior to a second-price auction, but may be profitable prior to a first-price auction. However, a sequence of offers is profitable in either type of auction. In our model, suitably chosen pre-auction offers work because they move the assignment when bidder valuations are “near the top” closer to the optimal, revenue-maximizing assignment.     

Deterring collusion with a reserve price: an auction experiment

Experimental Economics - We experimentally compare collusive behaviors in first-price sealed-bid auctions without and with a reserve price. Before the auction begins, a bidder may offer a bribe to...     

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.     

Auction Design for the Allocation of Emission Permits in the Presence of Market Power

To the extent that emission permits have been allocated using market mechanisms, this has been done using a sealed-bid auction design, typically with discriminatory prices. However, several authors have recommended the ascending auction format. Basically, two competing ascending auction designs have been suggested, the standard ascending auction (with clock or demand schedules), or an alternative ascending-clock implementation of Vickrey-pricing. The latter design was introduced as a response to problems of bid shading under the sealed-bid and the standard ascending auction format. The purpose of this paper is to investigate the allocation of permits under these two alternative mechanisms. The auction process and the resulting market outcome in the presence of oligopolistic competition are simulated. In this setting, it is not obvious that bid shading is the optimal strategy under the standard design, nor is it obvious that sincere bidding is the optimal strategy under the alternative ascending auction design. The alternative auction format makes it less costly to pursue a strategy to increase market shares through the acquisition of emission permits, thus increasing the competitor's costs, leading to overbidding as the optimal strategy.     

A Simple Model of Expert and Non-Expert Bidding in First-Price Auctions

This paper studies the equilibrium bidding behavior in a first-price sealed-bid auction when the number of informed bidders is not common knowledge. Both the independent private values and the common value cases are analyzed, under the assumption that a “neutral” signal exists. In equilibrium, experts and non-experts draw their bids from distinct supports: experts bid in the upper and lower tail of the bidding distribution and non-experts randomize their bids in between. For common values, it is shown that the seller's expected revenue always decreases with the probability of a bidder being informed when this probability is small. The opposite result is shown for the case of independent private values.Journal of Economic LiteratureClassification Numbers: D44, D82.     

The symmetric multiple prize all-pay auction with complete information

This paper extends the analysis of the n-player all-pay auction with complete information to cover the case of m≤n prizes, valued in weakly decreasing order, but symmetrically across players. We provide a complete characterization of the Nash equilibrium distributions for this class of auctions and provide an exact expression for the expected revenue generated.     

Asymmetric information about rivals'' types in standard auctions

We study auctions in which bidders may know the types of some rival bidders but not others. This asymmetry in bidders' knowledge about rivals' types has different effects on the two standard auction formats. In a second-price auction, it is weakly dominant to bid one's valuation, so the knowledge of rivals' types has no effect, and the good is allocated efficiently. In a first-price auction, bidders refine their bidding strategies based on their knowledge of rivals' types, which yields an inefficient allocation. We show that the inefficient allocation in the first-price auction translates into a poor revenue performance. Given a standard regularity condition, the seller earns higher expected revenue from the second-price auction than from the first-price auction, whereas the bidders are better off from the latter.     

Endogenous Entry and Exit in Common Value Auctions

We develop and experimentally test a model of endogenous entry, exit, and bidding in common value auctions. The model and experimental design include an alternative profitable activity (a safe haven) that provides agentspecific opportunity costs of bidding in the auction. Each agent chooses whether to accept the safe haven income or forgo it in order to bid in the auction. Agents that enter the auction receive independently-drawn private signals that provide unbiased estimates of the common value. The auctioned item is allocated to the high bidder at a price that is equal to the high bid. Thus the market is a first-price sealed-bid common value auction with endogenous determination of market size.     

Best-of-three all-pay auctions

We study a best-of-three all-pay auction. It is shown that with values of winning and without values of losing, this auction is less productive (the players’ total expected effort is smaller) than the one-stage all-pay auction. However, with different values of losing over the contest’s stages it may be more productive than the one-stage all-pay auction.     

A Sealed-Bid Auction That Matches the English Auction

This paper analyzes a two-stage sealed-bid auction that is frequently employed in privatization, takeover, and merger and acquisition contests. This auction format yields the same expected revenue as the open ascending (English) auction, yet is less susceptible to preemptive bidding and collusion. Journal of Economic Literature Classification Number: D44.     

Multi-dimensional reference-dependent preferences in sealed-bid auctions – How (most) laboratory experiments differ from the field

We study bidding behavior in first- and second-price sealed-bid auctions with loss-averse agents. Our model predicts overbidding in first-price induced-value auctions consistent with evidence from most laboratory experiments. Substantially different bidding behavior could result in commodity auctions where money and auction item are consumed along different dimensions of the consumption space. Differences also result in second-price auctions. Our study thereby indicates that transferring qualitative behavioral findings from induced-value laboratory experiments to the field may be problematic if subjects are loss-averse.     

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.     

Moral Hazard and Adverse Selection in Procurement Contracting

A model of procurement contracting is developed and tested in laboratory experiments. Market performance results are presented for both fixed-price and cost-sharing contracts. Contracts are awarded with first-price sealed-bid or second-price sealed-bid auctions. The environment contains post-auction cost uncertainty and opportunity for unmonitored effort in contract cost reduction. Cost-sharing contracts are found to reduce procurement expense but also to be inefficient because of their induced moral hazard waste and cost overruns.Journal of Economic LiteratureClassification Numbers: C72, C92, D44, D61, D82, H57, L14.     

Time is money: The effect of clock speed on seller’s revenue in Dutch auctions

We study the role of timing in auctions under the premise that time is a valuable resource. When one object is for sale, Dutch and first-price sealed bid auctions are strategically equivalent in standard models, and therefore, they should yield the same revenue for the auctioneer. We study Dutch and first-price sealed bid auctions in the laboratory, with a specific emphasis on the speed of the clock in the Dutch auction. At fast clock speeds, revenue in the Dutch auction is significantly lower than it is in the sealed bid auction. When the clock is sufficiently slow, however, revenue in the Dutch auction is higher than the revenue in the sealed bid auction. We develop and test a simple model of auctions with impatient bidders that is consistent with these laboratory findings.

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