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Description
The value of an asset is generally not known a priori, and it requires costly investments to be discovered. In such contexts with endogenous information acquisition, which selling procedure generates more revenues? We show that dynamic formats, such as ascending-price or multistage auctions, perform better than their static counterpart. This is because dynamic formats allow bidders to observe the number of competitors left throughout the selling procedure. Thus, even if competition appears strong ex ante, it may turn out to be weak along the dynamic format, thereby making the option to acquire information valuable. This very possibility also induces the bidders to stay longer in the auction, just to learn about the state of competition. Both effects boost revenues, and our analysis provides a rationale for using dynamic formats rather than sealed-bid ones.
1. Introduction
* Assessing the value of an asset for sale is a costly activity. When a firm is being sold, each individual buyer has to figure out the best use of the assets, which business unit to keep or resell, which site or production line to close. The resources spent can be very large when there is no obvious way for the buyer to combine the asset for sale with the assets that he already owns. Similarly, when acquiring a license for digital television, entrants have to figure out the type of program they will have a comparative advantage on, as well as the advertisement revenues they can expect from the type of program they wish to broadcast. Incumbents may also want to assess the economies of scale that can be derived from the new acquisition. All such activities are aimed at refining the assessment of the valuation of the license, and they are costly.
From the seller's perspective, if the assets are auctioned to a set of potential buyers/bidders, the better informed the bidders are, the higher the revenues, at least when the number of competitors is not too small. (l) However, when information is costly to acquire, a potential buyer may worry about the possibility that he spends many resources and yet ends up not winning the asset. Providing the bidders with incentives to acquire information is thus key for the seller.
One commonly used format for selling assets is the sealed-bid auction, in which the winner is selected in a single round. Other formats (which are frequently used when the asset is complex) are multistage auctions and ascending-price auctions, in which the number of potential buyers is gradually reduced. (2) In the sealed-bid format, information acquisition may only take place prior to the auction. In dynamic formats, information acquisition may take place not only prior to the auction but also in the course of the auction.
Our objective is to compare dynamic- and static-auction formats in settings in which some bidders initially know their valuations while others have the option to acquire further information on their valuation at some cost. (3)
The main insight of this paper is that dynamic-auction procedures are likely to generate more information acquisition and higher revenues than their static counterparts. (4) More precisely, we highlight a significant benefit induced by formats in which bidders gradually get to know the number of (serious) competitors they are facing, which in turn allows them to better adjust their information-acquisition strategy.
To get some intuition for our insight, observe that, in the sealed-bid static format, bidders do not acquire information on their valuations whenever there are too many competitors. The point is that the risk of ending up not buying the good (because it turns out that someone else has a higher value) is then so large that bidders prefer not to waste their money (or time) on getting such precise information. In contrast, in the ascending-price auction format, bidders get to obtain a better estimate of their chance of winning just by observing the number of bidders left. In particular, even if competition appears strong ex ante, it may turn out to be weak (if many bidders drop out), and information acquisition may then become a valuable option.
This has two effects. First, it generates more information acquisition (hence, more revenues-at least when the number of bidders is not too small). Second, it may induce bidders to wait and remain active in the auction, just to learn more about the state of competition. The latter effect also raises the price paid by winners, hence revenues, as compared with the price paid in the sealed-bid format.
It should be emphasized that the reason why dynamic formats generate more revenues here is completely different from the classic reason of affiliated values (Milgrom and Weber, 1982), in which ascending formats allow the bidders to learn about the information held by others. Here, the valuations of bidders are not influenced by other bidders' information (we consider a private-value setting), and yet dynamic-auction formats generate higher revenues (by modifying bidders' information-acquisition strategy on their own valuations).
Our paper can thus be viewed as providing a (new) rationale for using dynamic-auction formats. But note that our discussion has highlighted the role of providing bidders with some estimate of the level of competition (through the number of competitors left), and not all dynamic formats have the property of conveying such an estimate. Dynamic formats that do not have this property are less desirable from the perspective of this paper. For the sake of illustration, consider the one-object ascending-price auction with secret drop-out in which bidders observe the current level of price but not how many competitors are left. This is the auction format studied in an independent work by Rezende (2005). As it turns out (see Section 5), in our model, in which the information-acquisition cost is assumed to be bounded away from 0, bidders do not acquire information on their valuations when there are sufficiently many competitors. So the ascending price auction with secret drop-out is equivalent to the sealed-bid auction and it is dominated by the ascending-price auction (in which bidders observe the number of bidders left) when there are sufficiently many bidders (see a subsequent section for further discussion on Rezende's paper).
[] Related literature. Our paper is related to various strands of literature in auction theory: the comparison of auction formats (and more precisely here the comparison of the second-price and ascending-price auction formats), the analysis of information acquisition in auctions and the literature on entry in auctions.
Concerning the comparison between auction formats, we mentioned earlier the work by Milgrom and Weber (1982), who showed that, in affiliated value settings, the ascending and sealed-bid formats differ because the information on others' signals conveyed in equilibrium differ; hence, the bidders' assessments of their valuation differ too. In the context of auctions with negative externalities (see Jehiel and Moldovanu, 1996), Das Varma (2002) has shown that the ascending format could (under some conditions) generate higher revenues than the sealed-bid (second-price) auction format (in the ascending format, a bidder may be willing to stay longer, so as to combat a harmful competitor if he happens to be the remaining bidder). (5)
Concerning information acquisition in auctions, the literature has (in contrast with our work) focused on sealed-bid types of auction mechanisms, and it has essentially examined efficiency issues. (6)
In a private-value model, Hausch and Li (1991) show that first-price and second-price auctions are equivalent in a symmetric setting (see also Tan, 1992). (7) Stegeman (1996) shows that second-price auction induces an ex ante efficient information acquisition in the single-unit independent private values case (see also Bergemann and Valimaki, 2002). However, in Compte and Jehiel (2000), it is shown that the ascending-price auction may induce an even greater level of expected welfare.
Models of information acquisition in interdependent value contexts (in static mechanisms) include Milgrom (1981), who studies second-price auctions; Matthew s (1977, 1984), who studies first-price auctions and analyzes in a pure common value context whether the value of the winning bid converges to the true value of the object as the number of bidders gets large; (8) Persico (2000), who compares incentives for information acquisition in the first-price and second-price auctions in the affiliated value setting; and Bergemann and Valimaki (2002), who investigate, in a general interdependent value context, the impact of ex post efficiency on the ex ante incentives for information acquisition.
Our paper is also related to the literature on endogenous entry in auctions, which includes McAfee and McMillan (1987), Harstad (1990) and Levin and Smith (1994). (9) In these models, each bidder makes an entry decision prior to the auction, at a stage where bidders do not know their valuation. The decision to enter allows the bidder to both participate in the auction and learn her valuation. These models thus combine the idea of participation costs and the idea of information acquisition. This should be contrasted with our model in which there is no participation cost but only a cost to acquire information on the valuation.
Finally, our work is also related to the literature on research contests (Fullerton and McAfee, 1998; and more recently, Che and Gale, 2001). The main virtue of the ascending-price auction identified in this paper is that it increases the incentives to acquire information as, for some realizations of signals, it allows the bidders to realize that competition is less tough than it would have seemed from an ex ante viewpoint. Likewise, Fullerton and McAfee (1998) and Che and Gale (2001) identify conditions under which it is a good idea from an efficiency viewpoint to reduce the number of contestants to just a few (in fact two) in an attempt to increase contestants' incentives to exert effort in the contest. (10)
The rest of the paper is organized as follows. Section 2 describes the basic model. Section 3 develops the basic analysis that paves the way to the revenue comparison performed in Section 4. Further discussion of our model appears in Section 5.
2. The model
* There is one object for sale, worth to the seller, and there are n potential risk-neutral buyers, indexed by i [member of] [??] = {1, ..., n}. Each bidder, i = 1, ..., n, has a valuation [[theta].sub.i] for the object. The valuations [[theta].sub.i] for the various bidders i are assumed to be drawn from independent and identical distributions, with support on a finite number of values [[theta].sup.k], k [member of] {1, ..., K}, with < [[theta].sub.i] < ... < [[theta].sub.k] < ... < [[theta].sub.i] = [??]. We denote by [f.sup.k] the corresponding probability that the valuation is [[thrat].sup.k]. (11)
In our model, there will be two types of buyers: the informed buyers, who know the realization of their own valuation; and the uninformed buyers, who may get informed about their own valuation at some cost c. One possible interpretation is that, for some bidders, information acquisition is costless; hence, they become informed. We assume that each bidder's informational state (whether he is informed or not) is private information. We denote by [n.sub.1] the number of informed bidders and by [n.sub.2] the number of uninformed buyers. We assume that bidders' informational states are drawn from a distribution with full support on ([n.sub.1], [n.sub.2]), [n.sub.1] + [n.sub.2] = n.
For the sake of comparative statistics on the number of bidders, we will also consider the symmetric case where initially, each bidder i is informed with some probability q [member of] (0, 1) and uninformed with probability 1 - q and where informational states are drawn from independent distributions.
When bidder i is uninformed, his expected valuation from acquiring the object is (12)
[upsilon] [equivalent to][k.summation over (k-1)][[theta].sup.k][f.sup.k] (1)
When he acquires information, bidder i learns the realization [[theta].sup.i]. Other bidders, however, do not observe that realization; they do not observe either whether information acquisition occurred. Finally, it will be convenient to denote by [[theta].sup.(1)], [[theta].sup.(2)], ..., [[theta].sup.(j)] the highest valuation, the second highest valuation, and the jth highest valuation, respectively, among the (initially) informed bidders. We define similarly [[theta].sup.(1).sub.u], [[theta].sup.(2).sub.u], ..., [[theta].sup.(j).sub.u] for the (initially) uninformed bidders, where [[theta].sup.(j).sub.u] is obtained using the... |
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