There are N ≥ 2 buyers who engage in the auction of a house. The buyers have a common valuation of the house, denoted by v, which is known to all. All buyers make a simultaneous bid. Let pr denote the bid by buyer n = 1,, N. The one with the highest bid wins the house. The winner receives payoff v – på. The other(s) receive zero payoff. If more than one buyer makes the same highest bid, then they have an equal chance of winning the house. Prove that: (a) (b) (c) - It is not a Nash Equilibrium (NE) if the highest bid is v and only one buyer bids this price. this price. It is not a NE if the highest bid is less than v. It is a NE that the highest bid is v and more than one buyer bids
There are N ≥ 2 buyers who engage in the auction of a house. The buyers have a common valuation of the house, denoted by v, which is known to all. All buyers make a simultaneous bid. Let pr denote the bid by buyer n = 1,, N. The one with the highest bid wins the house. The winner receives payoff v – på. The other(s) receive zero payoff. If more than one buyer makes the same highest bid, then they have an equal chance of winning the house. Prove that: (a) (b) (c) - It is not a Nash Equilibrium (NE) if the highest bid is v and only one buyer bids this price. this price. It is not a NE if the highest bid is less than v. It is a NE that the highest bid is v and more than one buyer bids
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
Problem 4MC
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Transcribed Image Text:There are N ≥ 2 buyers who engage in the auction of a house. The buyers have
a common valuation of the house, denoted by v, which is known to all. All buyers
make a simultaneous bid. Let pr denote the bid by buyer n = 1,, N. The one
with the highest bid wins the house. The winner receives payoff v – på. The other(s)
receive zero payoff. If more than one buyer makes the same highest bid, then they
have an equal chance of winning the house. Prove that:
(a)
(b)
(c)
-
It is not a Nash Equilibrium (NE) if the highest bid is v and only one
buyer bids this price.
this price.
It is not a NE if the highest bid is less than v.
It is a NE that the highest bid is v and more than one buyer bids
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