Optimal auctions with information acquisition

This paper studies optimal auction design in a private value setting with endogenous information gathering. We develop a general framework for modeling information acquisition when a seller wants to sell an object to one of several potential buyers, who can each gather information about their valuations prior to participation in the auction. We first demonstrate that the optimal monopoly price is always lower than the standard monopoly price. We then show that standard auctions with a reserve price remain optimal among symmetric mechanisms, but the optimal reserve price lies between the ex ante mean valuation of bidders and the standard reserve price in Myerson (1981). Finally, we show that the optimal asymmetric mechanism softens the price discrimination against “strong” bidders.     

Information structures in optimal auctions

A seller wishes to sell an object to one of multiple bidders. The valuations of the bidders are privately known. We consider the joint design problem in which the seller can decide the accuracy by which bidders learn their valuation and to whom to sell at what price. We establish that optimal information structures in an optimal auction exhibit a number of properties: (i) information structures can be represented by monotone partitions, (ii) the cardinality of each partition is finite, (iii) the partitions are asymmetric across agents. We show that an optimal information structure exists.     

Similar bidders in takeover contests

When bidders in a corporate takeover have related resources and post-acquisition strategies, their valuations of a target are likely to be interdependent. This paper analyzes sequential-entry takeover contests in which similar bidders have correlated private valuations. The level of similarity affects information content of bids and bidding competition. Our model predicts that expected acquisition prices and the probability of multiple-bidder contests are the highest for intermediately similar bidders. We test these predictions in laboratory experiments in which we control the similarity between bidders. The experimental data confirm the non-monotonic effects of similarity on prices and on the frequency of multiple-bidder contents.     

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.     

Banning Bidders from All-pay Auctions

We consider an all-pay auction with complete information among the bidders; the seller does not observe the bidders’ values. We show that for some information structures in which the seller has a small uncertainty about the valuations, it is profitable for him to exclude from the auction all but two (randomly selected) bidders even though the latter are ex ante identical from his point of view.I am grateful to Paolo Bertoletti who introduced me to this topic and provided useful comments. I also thank Dan Kovenock (Co-Editor) and two anonymous referees for suggestions which considerably improved the exposition.     

Equilibrium uniqueness with perfect complements

The present note analyzes the simultaneous ascending-bid auction with arbitrarily many asymmetric bidders with decreasing marginal valuations under complete information. We show that the game is solvable by iterated elimination of weakly dominated strategies if the efficient allocation assigns at least one unit to every player and if bid increments are sufficiently small. In that unique equilibrium, bidders immediately reduce their demand to the efficient allocation, and the auction ends in the first round of bidding.We would like to thank seminar participants at UC Davis, in particular Klaus Nehring and Louis Makowski for comments. Financial support by the Alexander–von–Humboldt Foundation through a Feodor–Lynen grant and by the Deutsche Forschungsgemeinschaft, SFB Transregio 15, “Governance and Efficiency of Economic Systems” is gratefully acknowledged.     

A near Pareto optimal auction with budget constraints

In a setup where a divisible good is to be allocated to a set of bidders with budget constraints, we introduce a mechanism in the spirit of the Vickrey auction. In the mechanism we propose, understating budgets or values is weakly dominated. Since the revenue is increasing in budgets and values, all kinds of equilibrium deviations from true valuations turn out to be beneficial to the auctioneer. We also show that ex-post Nash equilibrium of our mechanism is near Pareto optimal in the sense that all full winners? values are above all full losers? values.     

When curiosity kills the profits: An experimental examination

Economic theory predicts that in a first-price auction with equal and observable valuations, bidders earn zero profits. Theory also predicts that if valuations are not common knowledge, then since it is weakly dominated to bid your valuation, bidders will bid less and earn positive profits. Hence, rational players in an auction game should prefer less public information. We are perhaps more used to seeing these results in the equivalent Bertrand setting. In our experimental auction, we find that individuals without information on each other's valuations earn more profits than those with common knowledge. However, given a choice between the two sets of rules, approximately half the individuals preferred to have the public information. We discuss possible explanations, including showing that there is a correlation between ambiguity aversion and a preference for having more information in the auction.     

Competitive auctions

We study a class of single-round, sealed-bid auctions for an item in unlimited supply, such as a digital good. We introduce the notion of competitive auctions. A competitive auction is truthful (i.e. encourages bidders to bid their true valuations) and on all inputs yields profit that is within a constant factor of the profit of the optimal single sale price. We justify the use of optimal single price profit as a benchmark for evaluating a competitive auctions profit. We exhibit several randomized competitive auctions and show that there is no symmetric deterministic competitive auction. Our results extend to bounded supply markets, for which we also give competitive auctions.     

The value of information for auctioneers

An auctioneer wants to sell an indivisible object to one of multiple bidders, who have private information about their valuations of the object. A bidder's information structure determines the accuracy with which the bidder knows her private valuation. The main result of the paper is that the auctioneer's revenue is a convex function of bidders' information structures. One implication is that assigning asymmetric information structures instead of symmetric information structures to bidders is always revenue-enhancing. This paper generalizes a result of Bergemann and Pesendorfer [D. Bergemann, M. Pesendorfer, Information structures in optimal auctions, J. Econ. Theory 137 (2007) 580–609], who show that revenue-maximizing information structures are asymmetric.     

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.     

Auctioning Risky Conservation Contracts

Conservation auctions have the potential to increase the efficiency of payments to farmers to adopt conservation-friendly management practices by fostering competition among them. The literature considers bidders that have complete information about the costs of adoption and optimal bidding behavior reflects this information advantage. Farmers seek information rents and bids decrease when risk aversion increases because farmers are more averse to losing the auction. We contribute to the literature by allowing for cost risk. Our paper shows that farmers must balance the risk of losing the auction (thus foregoing information rent) with the risk of submitting a bid that is not high enough to pay the costs of adopting conservation practices (thus incurring losses). We design an experiment to trade off these two risks and examine how risk aversion affects bidding behavior when participants face different sources and levels of risk. Our experiment contributes to a small literature on experimental auctions with risky product valuations. We find that participants decrease their bids as risk aversion increases, even in auctions with cost risk, suggesting that the risk of losing the auction dominates. These findings uncover new challenges for the practical implementation of conservation auctions as an efficient policy instrument.     

Surplus extraction with rich type spaces

We characterize revenue maximizing mechanisms in auction settings with ‘rich’ type spaces, where bidders obtain information from sources other than their own valuation. By considering a relaxed problem, we provide an upper bound on revenue extraction that explicitly builds on the richness of the information structure. We provide a condition under which this upper bound is achieved and describe an optimal mechanism. Under this condition, we also show that the optimal revenue can be achieved through dominant strategy implementation.     

REPUTATIONAL BIDDING

We consider auctions where bidders care about the reputational effects of their bidding and argue that the amount of information disclosed at the end of the auction will influence bidding. We focus on bid disclosure rules that capture all of the realistic cases. We show that bidders distort their bidding in a way that conforms to stylized facts about takeovers/licence auctions. We rank the disclosure rules in terms of their expected revenues and find that, under certain conditions, full disclosure will not be optimal. First‐price and second‐price auctions with price disclosure are not revenue equivalent and we rank them.     

Auction theory adaptations for real life applications

We develop extensions to auction theory results that are useful in real life scenarios.1. Since valuations are generally positive we first develop approximations using the log-normal distribution. This would be useful for many finance related auction settings since asset prices are usually non-negative.2. We formulate a positive symmetric discrete distribution, which is likely to be followed by the total number of auction participants, and incorporate this into auction theory results.3. We develop extensions when the valuations of the bidders are interdependent and incorporate all the results developed into a final combined realistic setting.4. Our methods can be a practical tool for bidders and auction sellers to maximize their profits. The models developed here could be potentially useful for inventory estimation and for wholesale procurement of financial instruments and also non-financial commodities.All the propositions are new results and they refer to existing results which are stated as Lemmas.     

Optimal Multi-Object Auctions

This paper analyses optimal auctions of several objects. In the first model bidders have a binary distribution over their valuations for each object, in which case the optimal auction is efficient. The optimal auction takes one of two formats: either objects are sold in independent auctions, or a degree of bundling is introduced in the sense that the probability a bidder wins one object is increasing in her value for the other. The format of the optimal auction may depend upon the number of bidders. In the second model the restriction to binary distributions is relaxed, and the optimal auction is then inefficient.     

Optimal advertising of auctions

We study a symmetric independent private values auction model where the revenue-maximizing seller faces a cost cn of attracting n bidders to the auction. If the distribution of valuations possesses an increasing failure rate (IFR), the seller overinvests in attracting bidders compared to the social optimum. Conversely, if the distribution is DFR, the seller underinvests compared to the social optimum. If the distribution of valuations becomes more dispersed, both, a revenue- and a welfare-maximizing seller, attract more bidders.     

An elementary proof of the common maximal bid in asymmetric first-price and all-pay auctions

We prove that the maximal bid in asymmetric first-price and all-pay auctions is the same for all bidders. Our proof is elementary, and does not require that bidders are risk neutral, or that the distribution functions of their valuations are independent or smooth.     

Retailers and consumers in sequential auctions of collectibles

Abstract.  We analyse an independent private-value model, where heterogeneous bidders compete for objects sold in sequential second-price auctions. In this heterogeneous game, bidders may have differently distributed valuations, and some have multi-unit demand with decreasing marginal values (retailers); others have a specific single-unit demand (consumers). By examining equilibrium bidding strategies and price sequences, we show that the presence of consumers leads to more aggressive bidding from the retailers on average and heterogeneous bidders is a plausible explanation of the price decline effect. The study of the expected revenue of the seller confirms the interest of auctioneers in inviting different types of bidders.     

Auction fever: Rising revenue in second-price auction formats

The prevalent term “auction fever” visualizes that ascending auctions – inconsistent with theory – are likely to provoke higher bids than one-shot auctions. To explore and isolate causes of auction fever experimentally, we design four different strategy-proof auction formats and order these according to expected rising bids based on pseudo-endowment effect arguments (psychological ownership and disparity between willingness to pay and willingness to accept). Observed revenues in the experiment in the four formats rank as expected if bidders have private uncertain values (the private information of a bidder is the distribution of her value). A control treatment supports our view that the traditional private certain values approach prevents auction fever in the laboratory. Another control treatment with a procurement auction relates the auction fever bids to bids in a one-shot auction with real endowments. We conclude that, when bidders are uncertain about their valuations, auctions that foster pseudo-endowment may raise bids and revenues.