Auctions with uncertain numbers of bidders

We investigate bidders’ and seller's responses to ambiguity about the number of bidders in the first price auction (FPA) and the second price auction (SPA) with independent private valuations. We model ambiguity aversion using the maxmin expected utility model. We find that bidders prefer the number of bidders to be revealed in the FPA, are indifferent between revealing and concealing in the SPA, and prefer the SPA to the FPA. If bidders are more pessimistic than the seller then the seller prefers to conceal the number of bidders in the FPA, and prefers the FPA to the SPA.     

Auctions with a random number of identical bidders

We examine and compare the (normally, mixed) symmetric equilibrium bidding strategies in first-price and all-pay common value multiple item auctions with a random number of bidders, who only seek one of the identical items and have the same budget.     

Auctions with private uncertainty and resale opportunities

When an auction is followed by an opportunity for resale, bidder valuations are endogenously determined, reflecting anticipated profit from buying/selling in the resale market. These valuations vary with the resale market structure, can differ across auction types, and may be lower or higher than if resale were impossible. Although resale introduces a common value element to the model, revenue equivalence can hold; when it fails, this is due not to affiliation but to differences in information conveyed to the secondary market. Information linkages between markets can also lead to signaling and, in some cases, preclude separation in the auction.     

Equilibrium of a sequence of auctions when bidders demand multiple items

We construct an ex post perfect equilibrium in a sequence of second-price auctions with two bidders where each bidder’s marginal values for additional units are decreasing. This equilibrium implies an increasing path of transaction prices and is ex post efficient.     

First-price sealed-bid auctions when bidders exhibit different attitudes toward risk

When bidders have different risk aversion levels, we determine in a first-price auction, the asymmetric equilibrium strategies. We analyze the impact of asymmetric risk aversion levels on bidders’ markups and on the expected revenue and allocative efficiency of the auction.     

Auctions with both common-value and private-value bidders

This paper shows the existence of monotone pure-strategy equilibrium in auctions with both common-value bidders and private-value ones. In equilibrium, the common-value bidders bid less aggressively when there are more private-value bidders. Further, resale is discussed as an application.     

Auctions with endogenous participation and an uncertain number of bidders: experimental evidence

Attracting bidders to an auction is a key factor in determining revenue. We experimentally investigate entry and bidding behavior in first-price and English clock auctions to determine the revenue implications of entry. Potential bidders observe their value and then decide whether or not to incur a cost to enter. We also vary whether or not bidders are informed regarding the number of entrants prior to placing their bids. Revenue equivalence is predicted in all four environments. We find that, regardless of whether or not bidders are informed, first-price auctions generate more revenue than English clock auctions. Within a given auction format, the effect of informing bidders differs. In first-price auctions, revenue is higher when bidders are informed, while the opposite is true in English clock auctions. The optimal choice for an auction designer who wishes to maximize revenue is a first-price auction with uninformed bidders.     

Uniqueness in symmetric first-price auctions with affiliation

The first-price auction has a unique monotone pure strategy equilibrium when there are n symmetric risk-averse bidders having affiliated types and interdependent values.     

The all-pay auction with complete information

Summary In a (first price) all-pay auction, bidders simultaneously submit bids for an item. All players forfeit their bids, and the high bidder receives the item. This auction is widely used in economics to model rent seeking, R&D races, political contests, and job promotion tournaments. We fully characterize equilibrium for this class of games, and show that the set of equilibria is much larger than has been recognized in the literature. When there are more than two players, for instance, we show that even when the auction is symmetric there exists a continuum of asymmetric equilibria. Moreover, for economically important configurations of valuations, there is no revenue equivalence across the equilibria; asymmetric equilibria imply higher expected revenues than the symmetric equilibrium.We are grateful to Jacques Crémer, Chuangyin Dang, Jürgen Dennert, Chaim Fershtman, Martin Hellwig, Arthur Robson, Heinrich Ursprung, Eric van Damme, Ton Vorst, and the referees for helpful comments. We benefitted from presentations at the World Congress of the Econometric Society in Barcelona, the European Meeting on the Economics of Information at Tilburg University, the Midwest Mathematical Economics Meetings at the University of Illinois, and seminars at Texas A&M University, The Pennsylvania State University, Tilburg University and the University of Montreal. Baye is grateful for support from the CentER for Economic Research at Tilburg University and the Tinbergen Institute where earlier versions of this paper were completed. Kovenock acknowledges support from Erasmus Universiteit Rotterdam, the Tinbergen Institute, the Center for Economic Studies at the University of Munich, the Institut d'Analisi Economica CSIC at the Universitat Autonoma de Barcelona, the Krannert School of Management, and the Jay N. Ross Young Faculty Scholar Award.     

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.     

Matching auction with winner’s curse and imperfect financial markets

This paper explains how and why the Matching Auctions work better with Imperfect Financial Markets. We show that an efficient outsider can obtain a “good” project even if the insider has informational advantage.     

Charity auctions with multiple goods: Bidding behavior and revenue

In a charity auction with multiple goods, we show that the highest-losing bid uniform price auction revenue dominates its lowest-winning bid counterpart. Only in the highest-losing bid uniform price auction is bidding independent of the number of goods and players and revenue increasing in the number of goods.     

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.     

Asymmetric auctions with resale: An experimental study

We study auctions with resale based on Hafalir and Krishna's (2008) [6] model. As predicted, weak bidders bid more with resale than without, so that average auction prices tend to increase. When the equilibrium calls for weak types to bid higher than their values with resale they do, but not nearly as much as the theory predicts. In other treatments outcomes are much closer to the risk neutral Nash model's predictions. Bid distributions for weak and strong types are more similar with resale than without, in line with the theory.     

Branching bandits: a sequential search process with correlated pay-offs

This paper presents a model of a sequential search process for the best outcome of many multi-stage projects. The branching structure of the search environment is such that the payoffs to various actions are correlated; nevertheless, it is shown that the optimal strategy is given by a simple reservation price rule.     

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.