Academic journal article Economic Inquiry

Entry Coordination and Auction Design with Private Costs of Information Acquisition

Academic journal article Economic Inquiry

Entry Coordination and Auction Design with Private Costs of Information Acquisition

Article excerpt

I. INTRODUCTION

In most auction literature, bidders are passively endowed with private information about their valuations. The analysis then focuses on optimal elicitation of private information. On many occasions, bidders may instead have to incur costs to collect this information. (1) Auction design in these cases has to balance between information acquisition and information elicitation, which are interdependent. The performance of an auction depends not only on the bidding equilibrium but also crucially on the information acquisition equilibrium. (2) As a salient feature, auction design with information acquisition costs has been complicated by entry coordination among bidders due to multiple entry equilibria issue. In a symmetric independent private value (IPV) setting of McAfee and McMillan (1987) with fixed information acquisition cost, Levin and Smith (1994) note that the ex ante efficient and revenue-maximizing auction (a second-price auction with no entry fee and no reserve) induces many asymmetric entry equilibria other than the targeted symmetric one. The existence of asymmetric entry equilibria in this setup fundamentally lies in bidders' constant marginal cost of entry. (3)

Information acquisition costs could be private information of bidders just as with their private information about values. For example, in the cases of construction procurements or U.S. timber auctions, many aspects of prebid information acquisition and analyzation are private knowledge of bidders. (4) Clearly, when information acquisition costs are private information of bidders, auction design has to additionally take into account information elicitation at the information acquisition stage. This aspect of analysis has yet to be reflected in the literature, while the case with fixed information acquisition costs has been thoroughly studied by Milgrom (1981), McAfee and McMillan (1987), Engelbrecht-Wiggans (1987, 1993), Harstad (1990), Levin and Smith (1994), McAfee, Quan, and Vincent (2002), Ye (2004, 2007), and Cremer, Spiegel, and Zheng (2009) among others. A widely recognized insight of these studies is that ex ante efficiency can be achieved through a second-price auction while setting the reserve at the seller's valuation. If ex ante entry fees can be used to extract all the expected surplus of bidders then there is a congruence between the revenue and total surplus. (5) This article advances this line of research by studying the implications of private acquisition costs on auction design with an emphasis on bidders' coordination at the information acquisition stage. Specifically, we consider the IPV setting of McAfee and McMillan (1987) and Levin and Smith (1994) while allowing the information acquisition costs to be bidders' private information, which follow a continuous distribution. In light of our previous discussion, this article attempts to answer the following questions: (1) How are ex ante efficient and revenue-maximizing auctions affected by this additional dimension of private information? In other words, how does information rent extraction at the entry stage affect the auction designs? (2) Can this private information alleviate (rather than aggravate) the problem of entry coordination? With the dispersion in private information acquisition costs, the multiplicity of entry equilibria arising from the constant marginal cost in Levin and Smith (1994) might be avoidable. The types with higher information acquisition costs must have less incentive to enter, which could reduce the number of entry equilibria. The questions are: Will sufficient dispersion coordinate bidders and induce a unique entry? If yes, how much dispersion is enough?

Due to the potential multiplicity of entry equilibria for any given mechanism, it is rather difficult to compare performances across varieties of mechanisms. To overcome this difficulty, we come up with an alternative approach. Our analysis begins with characterizing efficient and revenue-maximizing auctions for any given feasible entry pattern, which can be described through a vector of bidders' entry thresholds of acquisition costs. …

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