Imagine a seller (auctioneer) wanting to sell an item. There are two potential buyers, bidder 1 and bidder 2. Let v₁ and v₂ denote the valuations of the bidders. If bidder i wins the painting and has to pay x for it, then bidder i's payoff is vi-x. The bidders observe their own valuations before the auction. However, they do not observe each other's valuation, but know that the other valuation can be between 0 to 90. Consider now a second-price sealed bid auction. In this auction, players simultaneously and independently submit their bids b₁ and b₂. The painting is awarded to the highest bidder at a price equal to the second-highest bid. Show that the (weakly) dominant strategy for the players is to bid their own valuation (i.e. b=v), and this is the profile which will constitute the Bayesian Nash equilibrium of this game. (
Imagine a seller (auctioneer) wanting to sell an item. There are two potential buyers, bidder 1 and bidder 2. Let v₁ and v₂ denote the valuations of the bidders. If bidder i wins the painting and has to pay x for it, then bidder i's payoff is vi-x. The bidders observe their own valuations before the auction. However, they do not observe each other's valuation, but know that the other valuation can be between 0 to 90. Consider now a second-price sealed bid auction. In this auction, players simultaneously and independently submit their bids b₁ and b₂. The painting is awarded to the highest bidder at a price equal to the second-highest bid. Show that the (weakly) dominant strategy for the players is to bid their own valuation (i.e. b=v), and this is the profile which will constitute the Bayesian Nash equilibrium of this game. (
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
Chapter16: Bargaining
Section: Chapter Questions
Problem 16.1IP
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Transcribed Image Text:Imagine a seller (auctioneer) wanting to sell an item. There are two potential buyers, bidder 1
and bidder 2. Let v₁ and v₂ denote the valuations of the bidders. If bidder i wins the painting
and has to pay x for it, then bidder i's payoff is vi-x. The bidders observe their own valuations
before the auction. However, they do not observe each other's valuation, but know that the
other valuation can be between 0 to 90. Consider now a second-price sealed bid auction. In this
auction, players simultaneously and independently submit their bids b₁ and b₂. The painting is
awarded to the highest bidder at a price equal to the second-highest bid. Show that the (weakly)
dominant strategy for the players is to bid their own valuation (i.e. b;=v₁), and this is the profile
which will constitute the Bayesian Nash equilibrium of this game. (
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