First-Price and Second-Price Auctions - Consider an auction of a single indi- visible object with 5 bidders, 1, 2, 3, 4 and 5, whose personal valuations (willingness to pay) for the object are v₁ 10, V₂ = 8, V3 = 7, V4 5 and v5 3. The bidders simultaneously submit their bids and the winner is the one with the highest bid. = Suppose that, when the highest bidder is not unique, the bidder with the smallest number (highest valuation) wins. (a) Suppose that this is a second-price auction, where the winner pays the highest bid among those from her opponents, determine whether each of the following ilibrium Explain bidding profil in a Noch =

First-Price and Second-Price Auctions - Consider an auction of a single indi- visible object with 5 bidders, 1, 2, 3, 4 and 5, whose personal valuations (willingness to pay) for the object are v₁ 10, V₂ = 8, V3 = 7, V4 5 and v5 3. The bidders simultaneously submit their bids and the winner is the one with the highest bid. = Suppose that, when the highest bidder is not unique, the bidder with the smallest number (highest valuation) wins. (a) Suppose that this is a second-price auction, where the winner pays the highest bid among those from her opponents, determine whether each of the following ilibrium Explain bidding profil in a Noch =

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

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First-Price and Second-Price Auctions - Consider an auction of a single indi-
visible object with 5 bidders, 1, 2, 3, 4 and 5, whose personal valuations (willingness
to pay) for the object are v₁ = 10, V₂ = 8, 03
7, 04 5 and 5
3. The bidders
simultaneously submit their bids and the winner is the one with the highest bid.
Suppose that, when the highest bidder is not unique, the bidder with the smallest
number (highest valuation) wins.
(a) Suppose that this is a second-price auction, where the winner pays the highest
bid among those from her opponents, determine whether each of the following
bidding profiles is a Nash equilibrium. Explain.
(i) (b₁,b2, b3, b4, b5) = (10, 8, 7, 5, 3)
(ii) (b1,b2, b3, b4, b5) = (8,8, 0, 0, 0)
(iii) (b₁,b2, b3, b4, b5) = (10, 0, 0, 0, 10)
(b) Now suppose that this is a first-price auction, where the winner pays their own
bid, determine whether each of the bidding profiles above is a Nash equilibrium.
Explain.
=
=

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