3. Consider an all-pay auction in which the two bidders' values are uniformly distributed between [0, 1]. The optimal bidding strategy for each bidder is b* (v) =v²/2. (a) Show that the seller's expected revenue is the same as that in a first-price and second- price auction. [Hint: you don't need to use order statistics.]

Managerial Economics: A Problem Solving Approach
5th Edition
ISBN:9781337106665
Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Chapter18: Auctions
Section: Chapter Questions
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3. Consider an all-pay auction in which the two bidders' values are uniformly distributed
between [0, 1]. The optimal bidding strategy for each bidder is b' (v) = v/2.
(a) Show that the seller's expected revenne is the same as that in a first-price and second-
price auction. [Hint: you don't need to use order statistics.]
Transcribed Image Text:3. Consider an all-pay auction in which the two bidders' values are uniformly distributed between [0, 1]. The optimal bidding strategy for each bidder is b' (v) = v/2. (a) Show that the seller's expected revenne is the same as that in a first-price and second- price auction. [Hint: you don't need to use order statistics.]
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