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Auction Theory: A Guide to the Literature
 JOURNAL OF ECONOMIC SURVEYS
, 1999
"... This paper provides an elementary, nontechnical, survey of auction theory, by introducing and describing some of the critical papers in the subject. (The most important of these are reproduced in a companion book, The Economic Theory of Auctions, Paul Klemperer (ed.), Edward Elgar (pub.), forthco ..."
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Cited by 354 (3 self)
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This paper provides an elementary, nontechnical, survey of auction theory, by introducing and describing some of the critical papers in the subject. (The most important of these are reproduced in a companion book, The Economic Theory of Auctions, Paul Klemperer (ed.), Edward Elgar (pub.), forthcoming.) We begin with the most fundamental concepts, and then introduce the basic analysis of optimal auctions, the revenue equivalence theorem, and marginal revenues. Subsequent sections address riskaversion, affiliation, asymmetries, entry, collusion, multiunit auctions, double auctions, royalties, incentive contracts, and other topics. Appendices contain technical details, some simple worked examples, and a bibliography for each section.
LogConcave Probability and its Applications
 Econom. Theory
, 1989
"... Many interesting propositions in the economics of information are built on the assumption that the log of the cumulative distribution function of a random variable is a concave function. This property is equivalent ..."
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Cited by 42 (1 self)
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Many interesting propositions in the economics of information are built on the assumption that the log of the cumulative distribution function of a random variable is a concave function. This property is equivalent
Identification of Standard Auction Models
, 2001
"... We present new identification results for models of firstprice, secondprice, ascending (English), and descending (Dutch) auctions. We analyze a general specification of the latent demand and information structure, nesting as special cases the pure private values and pure common values models, and ..."
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Cited by 41 (5 self)
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We present new identification results for models of firstprice, secondprice, ascending (English), and descending (Dutch) auctions. We analyze a general specification of the latent demand and information structure, nesting as special cases the pure private values and pure common values models, and allowing both ex ante symmetric and asymmetric bidders. We address identification of a series of nested models and derive testable restrictions that enable discrimination between models on the basis of observed data. The simplest model–that of symmetric independent private values–is nonparametrically identified even if only the transaction price from each auction is observed. For more complex models, identification and testable restrictions are obtained when additional information of one or more of the following types is available: (i) the identity of the winning bidder or other bidders, (ii) one or more bids in addition to the transaction price; (iii) exogenous variation in the number of bidders; (iv) bidderspecific covariates; (v) auctionspecific covariates. While many private values (PV) models are nonparametrically
Semiparametric Estimation of FirstPrice Auctions with Risk Averse Bidders
, 2000
"... This paper proposes a semiparametric estimation procedure of the firstprice auction model with risk averse bidders within the independent private values paradigm. We show that the model is nonidentified in general from observed bids. Moreover, any distribution of bids can be rationalized by an auct ..."
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Cited by 31 (1 self)
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This paper proposes a semiparametric estimation procedure of the firstprice auction model with risk averse bidders within the independent private values paradigm. We show that the model is nonidentified in general from observed bids. Moreover, any distribution of bids can be rationalized by an auction model with either constant relative risk aversion or constant absolute risk aversion. Thus identification of the model must be achieved through additional restrictions. We then establish semiparametric identification under a common but unknown support condition and parameterization of the bidders' utility function. Next we propose a semiparametric method for estimating the corresponding auction model using local polynomial estimators. This method involves several steps and allows to recover the parameters of the utility function as well as the bidders' private values and their distribution. An attractive computational advantage of our method is that it does not require solving the differential equation characterizing the equilibrium strategy. An illustration of the method on U.S. Forest Service timber sales is proposed. In particular, a test of bidders' risk neutrality is performed.
Resource selection games with unknown number of players
, 2006
"... In the context of preBayesian games we analyze resource selection games with unknown number of players. We prove the existence and uniqueness of a symmetric safetylevel equilibrium in such games and show that in a game with strictly increasing linear cost functions every player benefits from the c ..."
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Cited by 28 (9 self)
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In the context of preBayesian games we analyze resource selection games with unknown number of players. We prove the existence and uniqueness of a symmetric safetylevel equilibrium in such games and show that in a game with strictly increasing linear cost functions every player benefits from the common ignorance about the number of players. In order to perform the analysis we define safetylevel equilibrium for preBayesian games, and prove that it exists in a compactcontinuousconcave setup; in particular it exists in a finite setup. 1
A note on auctions with endogenous participation
 REVIEW OF ECONOMIC DESIGN
, 1996
"... In this paper, we study an auction where bidders only know the number of potential applicants. After seeing their values for the object, bidders decide whether or not to enter the auction. Players may not want to enter the auction since they have to pay participation costs. We characterize the optim ..."
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Cited by 22 (0 self)
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In this paper, we study an auction where bidders only know the number of potential applicants. After seeing their values for the object, bidders decide whether or not to enter the auction. Players may not want to enter the auction since they have to pay participation costs. We characterize the optimal bidding strategies for both first and secondprice sealedbid auction when participation is endogenous. We show that only bidders with values greater than a certain cutoff point will bid in these auctions. In this context, both auctions generate the same expected revenue. We also show that, contrarily to the predictions of the fixedn literature, the seller’s expected revenue may decrease when the number of potential participants increases. In addition, we show that it is optimal for the seller to charge an entry fee, which contrasts greatly with results from the existing literature on auctions with entry.
Bidder Collusion
, 2004
"... Within the heterogeneous IPV model, we analyze bidder collusion at firstprice and secondprice auctions, allowing for withincartel transfers. Our focus is on cartels that contain a strict subset of all bidders and collusive mechanisms that do not rely on information from the auctioneer, such as th ..."
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Cited by 13 (0 self)
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Within the heterogeneous IPV model, we analyze bidder collusion at firstprice and secondprice auctions, allowing for withincartel transfers. Our focus is on cartels that contain a strict subset of all bidders and collusive mechanisms that do not rely on information from the auctioneer, such as the identity of the winner or the amount paid. We show that when a cartel cannot control the bids of its members, it can eliminate all competition among its members at a secondprice auction, but not at a firstprice auction. At a firstprice auction, when the cartel cannot control its members’ bids, cartel behavior is characterized by multiple cartel bids that are different but very close to one another. This finding has important empirical implications. If a cartel can control the bids of its members, it can suppress all ring competition at both a secondprice and a firstprice auction; however, if shill bidding is feasible, then a cartel at a firstprice auction does no better than one that cannot control its members’ bids.
Precautionary bidding in auctions
 Econometrica
, 2004
"... We analyze bidding behavior in auctions when riskaverse buyers bid for a good whose value is risky. We show that when the risk in the valuations increases, DARA bidders will reduce their bids by more than the appropriate increase in the risk premium. Ceteris paribus, buyers will be better off biddi ..."
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Cited by 11 (1 self)
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We analyze bidding behavior in auctions when riskaverse buyers bid for a good whose value is risky. We show that when the risk in the valuations increases, DARA bidders will reduce their bids by more than the appropriate increase in the risk premium. Ceteris paribus, buyers will be better off bidding for a more risky object in first price, second price, and English auctions with affiliated common (interdependent) values. This “precautionary bidding ” effect arises because the expected marginal utility of income increases with risk, so buyers are reluctant to bid so highly. We also show that precautionary bidding behavior can make DARA bidders prefer bidding in a common values setting to bidding in a private values one when riskneutral or CARA bidders would be indifferent. Thus the potential for a “winner’s curse ” can be a blessing for rational DARA bidders.
Comparing Open and Sealed Bid Auctions: Evidence from Timber Auctions.,” Quarterly
 Journal of Economics
"... Abstract. We study entry and bidding patterns in sealed bid and open auctions. Using data from U.S. Forest Service timber auctions, we document a set of systematic e¤ects: sealed bid auctions attract more small bidders, shift the allocation towards these bidders, and can also generate higher revenue ..."
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Cited by 8 (2 self)
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Abstract. We study entry and bidding patterns in sealed bid and open auctions. Using data from U.S. Forest Service timber auctions, we document a set of systematic e¤ects: sealed bid auctions attract more small bidders, shift the allocation towards these bidders, and can also generate higher revenue. A private value auction model with endogenous participation can account for these qualitative e¤ects of auction format. We estimate the model’s parameters and show that it can explain the quantitative e¤ects as well. We then use the model to assess bidder competitiveness, which has important consequences for auction design. We thank the editor Larry Katz and the referees for very helpful suggestions, and also Phil Haile, Jerry
ESTIMATING RISK AVERSION FROM ASCENDING AND SEALEDBID AUCTIONS: THE CASE OF TIMBER AUCTION DATA
, 2006
"... Estimating bidders’ risk aversion in auctions is a challeging problem because of identification issues. This paper takes advantage of bidding data from two auction designs to identify nonparametrically the bidders’ utility function within a private value framework. In particular, ascending auction d ..."
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Cited by 6 (0 self)
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Estimating bidders’ risk aversion in auctions is a challeging problem because of identification issues. This paper takes advantage of bidding data from two auction designs to identify nonparametrically the bidders’ utility function within a private value framework. In particular, ascending auction data allow us to recover the latent distribution of private values, while firstprice sealedbid auction data allow us to recover the bidders’ utility function. This leads to a nonparametric estimator. An application to the US Forest Service timber auctions is proposed. Estimated utility functions display concavity, which can be partly captured by constant relative risk aversion.