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DOI: 10.1007/s00199-004-0593-2Economic Theory 28, 449452 (2006)Department of Economics, Brock University, 500 Glenridge Avenue,
St. Catharines, Ontario, L2S 3A1, CANADA (e-mail: [email protected])Received: August 2, 2004; revised version: December 6, 2004Summary. Bulow and Klemperer [1] have provided an upper bound on the value
of bargaining power for a seller of an indivisible object. Specically, negotiating
optimally with N buyers yields lower revenue than an English auction with N +1
buyers. In this paper, a short and intuitive proof of this result is presented.Keywords and Phrases: Auctions, Negotiations, Rationing.JEL Classication Numbers: C78, D44, D82.Bulow and Klemperer [1] examine the value of bargaining power for the seller of
an indivisible good. At best, the seller can use his bargaining power to negotiate
optimally and attain the fully optimal revenue.1 On the other hand, running an
English auction with no reserve price demands no bargaining power on the part of
the seller. With symmetric buyers, Bulow and Klemperer [1] show that the English
auction with N +1 buyers yields strictly higher revenue than an optimal mechanism
with N buyers. Hence, the value of bargaining power is bounded above by the value
of an extra buyer. The aim of this paper is to provide a new, intuitive proof of this
result.Thus, consider a risk neutral seller with an indivisible object for sale, and normalize to zero the value the seller puts on consuming the good himself. The sellers
objective is to maximize revenue. In the following, a mechanism that maximizes
revenue among all mechanisms in which the object is sold with certainty will be[star] I would like to thank Per B. Overgaard and an anonymous referee for many valuable comments.1 In Bulow and Klemperers [1] terminology, optimal negotiation does not refer to a specic selling
procedure, but rather to an optimal mechanism. In this paper, we will generally, with the exception of
the English auction, abstract from the details of the selling procedure, by referring to it simply as a
mechanism.Exposita NotesA short proof of the Bulow-Klemperer auctions
vs. negotiations result[star]Ren
e Kirkegaard450 R. Kirkegaardsaid to be constrained optimal. In a fully optimal mechanism, on the other hand,
the object is not necessarily sold.2Before the seller stages a mechanism, each buyer receives a private signal from
some, commonly known, joint distribution....