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We consider a first-price auction when the ranking of bidders' private valuations is common knowledge among bidders. This new informational framework is motivated by several applications, from procurement to privatization. It induces a particular asymmetric auction model with affiliated private values that has several interesting properties but rai...
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In sequential auctions objects are sold one by one in separate auctions.
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strategies for these auctions. Theoretical models suggest that prices in
sequential auctions with private values or with randomly assig...
We study optimal bidder collusion at first-price auctions when the collusive mechanism only relies on signals about bidders’ valuations. We build on Fang and Morris (2006) when two bidders have low or high private valuation of a single object and additionally each receives a private noisy signal from an incentiveless center about the opponent’s val...
We develop econometric models of ascending (English) auctions which allow for both bidder asymmetries as well as common and/or private value components in bidders’ underlying valuations. We show that the equilibrium inverse bid functions in each round of the auction are implicitly defined (pointwise) by a system of nonlinear equations, so that cond...
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Citations
... Furthermore, we show that, in the first-price auction, the seller prefers those bidders who knows the value-rankings and can resell later, than to the symmetric bidders. From the policy point of view, the government can gain by revealing more information about the participants of the auction, while conducting spectrum licenses auction, procurement auction, etc. Landsberger et al. (2001) characterize and prove the existence of a unique Bayesian equilibrium in the first-price auction when only feature (a) is present. Feature (b) has been considered by Krishna (2008, 2009), Virág (2013Virág ( , 2016; Lebrun (2010), Cheng and Tan (2010), and Cheng (2006). ...
Consider a single-unit auction with resale and two risk neutral bidders. The ranking of the valuations is known to both the bidders—that is, the bidders know the identity of the highest and lowest valuation bidders. We show that, when the value-rankings are revealed, the classic result of “bid symmetrization” does not hold. Surprisingly, the bidder with the lowest valuation produces a stronger bid distribution than the bidder with the highest valuation. We also show that the revelation of value-rankings in auctions with resale asymmetrizes the bidding strategies. Finally, for a special family of probability distributions, we show that the first-price auction is revenue superior to the second-price auction.
... 6 Our study is also related to the literature on information revelation in auctions (Gershkov 2009;Kaplan 2012;Milgrom and Weber 1982;Persico 2000). Several papers study revelation of information about bidders' valuations by the auctioneer (Bergemann and Pesendorfer 2007;Eső and Szentes 2007;Kaplan and Zamir 2000;Landsberger et al. 2001). As in our study, Fang and Morris (2006) and Kim and Che (2004) compare first-and secondprice mechanisms but focus on value revelation rather than on leaked bids. ...
In sequential first‐ and second‐price private value auctions, second movers are informed about the first movers' bid with commonly known probability. Equilibrium bidding in first‐price auctions is mostly unaffected, but there are multiple equilibria in second‐price auctions affecting comparative statics across price rules. We show experimentally that informational leaks in first‐price auctions qualitatively confirm the theoretical predictions. In second‐price auctions, we analyze and experimentally confirm the existence of focal equilibria, and provide evidence for individual consistency in equilibrium selection. (JEL D44, C72, C91)
... Since the cost structures of inframarginal and extramarginal plants differ substantially (see Section 3.2), we would have to consider an asymmetric auction-theoretical model. However, the literature on these type of models shows the difficulties of their analysis concerning the existence and uniqueness of equilibria and the generality of the results (Maskin and Riley, 2000;Landsberger et al., 2001;Krishna, 2002). We therefore decided to develop a model with symmetric bidders, which provides a first benchmark for an idealized market with only inframarginal plants. ...
The shift towards renewable energies is accompanied by great volatility on the supply side, de- manding European-wide instead of national balancing services. For the integrated European procurement of balancing reserves, the European Commission proposes a multi-attributive auction mechanism which is very similar to the current German auction. The key difference, however, is a switch from pay-as-bid to uniform pricing. We develop a game-theoretical model of the current German and the future European balancing market design. Both market de- signs have desirable economic properties in their one-shot version, i.e., an efficient auction outcome and competitive prices. We show that a switch to uniform pricing does not induce bidders to report their true costs in their bids, but leads to underbidding. We contrast the equilibrium outcomes with German market data and find a substantial discrepancy, i.e., non- competitive prices. We provide a game-theoretical grounded explanation that is based on the regular repetition of the auction combined with the invariant supplier side.
... This paper is also related to a large literature on information revelation in auctions (Milgrom and Weber, 1982;Persico, 2000;Kaplan, 2012;Gershkov, 2009). Several papers study revelation of information about the bidders' valuation by the auctioneer (Kaplan and Zamir, 2000;Landsberger et al., 2001;Bergemann and Pesendorfer, 2007;Eső and Szentes, 2007). As in our study, Fang and Morris (2006) and Kim and Che (2004) compare the first-price and second-price mechanisms, but consider revelation of valuations rather than bids. ...
We study first- and second-price private value auctions with sequential bidding where second movers may discover the first movers’ bid. There is a unique equilibrium in the first-price auction and multiple equilibria in the second-price auction. Consequently, comparative statics across price rules are equivocal. We experimentally find that in the first-price auction, leaks benefit second movers but harm first movers and sellers. Low to medium probabilities of leak eliminate the usual revenue dominance of first-price over second-price auctions. With a high probability of a leak, second-price auctions generate higher revenue.
... Landsberger et.al [2] in the paper "First-Price Auctions when the Ranking of Valuations is Common Knowledge" studied a one unit two bidders game where the valuations ranking is known. At the beginning of the game, the valuations are drawn from a distribution that is common knowledge and the seller announces who is the bidder with the highest valuation. ...
In auction theory, cryptography has been used to achieve anonymity of the
participants, security and privacy of the bids, secure computation and to
simulate mediator (auctioneer). Auction theory focuses on revenue and
Cryptography focuses on security and privacy. Involving Cryptography at base
level, to enhance revenue gives entirely new perspective and insight to Auction
theory, thereby achieving the core goals of auction theory. In this report, we
try to investigate an interesting field of study in Auction Theory using
Cryptographic primitives.
... They also show, by example, that the equilibrium bidding strategies can typically not be expressed as an analytic function, due to a singularity in the bidding function at the lower end of the valuations. Fevrier (2003) extends the analysis of Landsberger, Rubinstein, Wolfstetter, and Zamir (2001) from 2 to n bidders. He then compares the revenue generated by the sale of two identical units of an object in the sequential auction over two periods to the revenue when the units are sold as a bundle in a single auction. ...
... Landsberger, Rubinstein, Wolfstetter, and Zamir (2001), there is no hope in finding a closed-form expression for the strategies if values are drawn from an interval. Furthermore, because from one period to the next, the winner decreases his bid by some finite amount, there would be no common knowledge of valuations once bid trajectories cross. ...
We investigate the role of market transparency in repeated first-price auctions. We consider a setting with private and independent values across bidders. The values are assumed to be perfectly persistent over time. We analyze the first-price auction under three distinct disclosure regimes regarding the bid and award history. Of particular interest is the minimal disclosure regime, in which each bidder only learns privately whether he won or lost the auction at the end of each round. In equilibrium, the winner of the initial auction lowers his bids over time, while losers keep their bids constant, in anticipation of the winner’s lower future bids. This equilibrium is efficient, and all information is eventually revealed. Importantly, this disclosure regime does not give rise to pooling equilibria. We contrast the minimal disclosure setting with the case in which all bids are public, and the case in which only the winner’s bids are public. In these settings, an inefficient pooling equilibrium with low revenues always exists with a sufficiently large number of bidders.
... We also assumed that bidders observe all first auction bids before they bid in the second auction. If instead bidders could only learn whether they either won or lost the first auction, in some subgames bidders would know the rank order of valuations, as in Landsberger et al. (2001). ...
In a sequence of first-price auctions with stable private values bidders strategically conceal their private information until the last auction. We characterize equilibrium bidding and explore how such signal jamming affects the dynamics of equilibrium prices.
... We also assumed that bidders observe all first auction bids before they bid in the second auction. If instead bidders could only learn whether they either won or lost the first auction, in some subgames bidders would know the rank order of valuations, as in Landsberger et al., (2001) and Février, (2003). ...
In a recurring auction early bids may reveal bidders’ types, which in turn affects bidding in later auctions. Bidders take this into account and may bid in a way that conceals their private information until the last auction is played. The present paper analyzes the equilibrium of a sequence of ?rst-price auctions assuming bidders have stable private values. We show that signal-jamming occurs and explore the dynamics of equilibrium prices.
... 25 A reader familiar with the numerical analysis literature which analyzes the sensitivity of the roots of a polynomial with respect to small perturbations to its coefficients could legitimately have serious doubts about the practical relevance of our estimation procedure. 26 Such issues do not seem to prevent the usefulness of our analysis. Note that our application involves polynomials of low degree. ...
... 25 A rigorous formalization of this point is left for future research. 26 Wilkinson's polynomial u → 20 k=1 (u − k) is the classic example where a perturbation of 2 −23 in the second leading coefficient of a polynomial whose roots are distant from unity leads to first-order perturbations of the roots: the root at x = 20 grows to x ≈ 20.8 and the roots at x = 18 and x = 19 collide into a double root. See Gautschi (1973) and Mosier (1986) for more on this topic. ...
... Our approach can also be used for alternative asymmetric auction models with independent private signals as models with one informed bidder against a set of noninformed bidders (Engelbrecht-Wiggans et al. (1983), Hernando-Veciana and Tröge (2010)), models with collusion through a ring (Marshall and Marx (2007)) or finally the model developed by Landsberger et al. (2001) where the ranking of bidders' private valuations is common knowledge among bidders (but possibly not to the econometrician). The ideas sustaining our methodology could also be useful more generally beyond auction environments for applications as imperfect matching between data sets, possible new anonymous designs in experimental economics or the design of surveys for sensitive attributes. ...
We consider standard auction models when bidders' identities are not observed by the econometrician. First, we adapt the definition of identifiability to a framework with anonymous bids and we explore the extent to which anonymity reduces the possibility to identify private value auction models. Second, in the asymmetric independent private value model which is nonparametrically identified, we generalize Guerre, Perrigne and Vuong's estimation procedure [Optimal Nonparametric Estimation of First-Price Auctions, Econometrica 68 (2000) 525-574] and study the asymptotic properties of our multi-step kernel-based estimator. Third a test for symmetry is proposed. Monte Carlo simulations illustrate the practical relevance of our estimation and testing procedures for small data sets.
... Initial information is also statistically independent in Landsberger, Rubinstein, Zamir and Wolfstetter (2001), and in Kaplan and Zamir (2002). Landsberger, Rubinstein, Zamir and Wolfstetter (2001) show that when the seller knows the ranking of buyers'valuations and she makes it common knowledge, a …rst-price auction raises higher revenue than in the case where the seller does not disclose this information. Kaplan and Zamir (2002) also consider information revelation in …rstprice auctions, but allow for more general public disclosure policies than Landsberger, Rubinstein, Zamir and Wolfstetter (2001) allow. ...
We consider a revenue-maximizing seller who, before proposing a mechanism to sell herobject(s), observes a vector of signals correlated with buyersívaluations. Each buyer knows only the signal that the seller observes about him, but not the signals she observes about other buyers. The seller Örst chooses how to disclose her information and then chooses a revenue-maximizing mechanism. We allow for very general disclosure policies, that can be random, public, private, or any mixture of these possibilities. Through the disclosure of information privately, the seller can create correlation in buyersítypes, which then consist of valuations plus beliefs. For thestandard independent private values model, we show that information revelation is irrelevant: irrespective of the disclosure policy an optimal mechanism for this informed seller generates expected revenue that is equal to her maximal revenue under full information disclosure. For more general allocation environments that allow also for interdependent, for common values, and for multiple items, disclosure policies may matter, and the best the seller can do is to disclose no information at all.
