7. Three bidders have a private valuation drawn from a uniform distribution on [0,30] for a single item. The valuations are 10, 15 and 20 for bidders 1, 2 and 3 respectively. a) What are the bidders' equilibrium strategies in a second price auction? b) Show that for bidder

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter7: Nonlinear Optimization Models
Section7.3: Pricing Models
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7. Three bidders have a private valuation
drawn from a uniform distribution on [0,30]
for a single item. The valuations are 10, 15 and
20 for bidders 1, 2 and 3 respectively. a) What
are the bidders' equilibrium strategies in a
second price auction? b) Show that for bidder
2 no deviation from his strategy in a) would
be profitable. c) Who wins the auction and
how much do they pay? d) If instead the seller
uses a first price sealed bid auction, what are
the bidders' equilibrium strategies?
Transcribed Image Text:7. Three bidders have a private valuation drawn from a uniform distribution on [0,30] for a single item. The valuations are 10, 15 and 20 for bidders 1, 2 and 3 respectively. a) What are the bidders' equilibrium strategies in a second price auction? b) Show that for bidder 2 no deviation from his strategy in a) would be profitable. c) Who wins the auction and how much do they pay? d) If instead the seller uses a first price sealed bid auction, what are the bidders' equilibrium strategies?
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