Two bidders compete in a sealed-bid auction for a single indivisible object. For each bidder , the valuation of the object is uniformly distributed on [0, 1]. The valuations of the two bidders are independent. Each bidder knows her own valuation, but not the valuation of the other bidder. The bidders simultaneously submit bids b = [0, ∞), and whoever submits the higher bid wins the object and pays the average of the two bids. In case of a tie, each bidder wins the object with probability 1/2 and again the winner pays the average of the two bids. Find a Nash equilibrium of this game in which each bidder's strategy is linear in her valuation.
Two bidders compete in a sealed-bid auction for a single indivisible object. For each bidder , the valuation of the object is uniformly distributed on [0, 1]. The valuations of the two bidders are independent. Each bidder knows her own valuation, but not the valuation of the other bidder. The bidders simultaneously submit bids b = [0, ∞), and whoever submits the higher bid wins the object and pays the average of the two bids. In case of a tie, each bidder wins the object with probability 1/2 and again the winner pays the average of the two bids. Find a Nash equilibrium of this game in which each bidder's strategy is linear in her valuation.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![Two bidders compete in a sealed-bid auction for a single indivisible object. For each bidder
i, the valuation of the object is uniformly distributed on [0, 1]. The valuations of the two
bidders are independent. Each bidder knows her own valuation, but not the valuation of
the other bidder. The bidders simultaneously submit bids b = [0, ∞), and whoever submits
the higher bid wins the object and pays the average of the two bids. In case of a tie, each
bidder wins the object with probability 1/2 and again the winner pays the average of the two
bids. Find a Nash equilibrium of this game in which each bidder's strategy is linear in her
valuation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa1ab2968-d288-4fd8-b87c-74963c459231%2F018b7b27-3bf5-4114-a5bd-63a75907fb3e%2F4bcq1r8_processed.png&w=3840&q=75)
Transcribed Image Text:Two bidders compete in a sealed-bid auction for a single indivisible object. For each bidder
i, the valuation of the object is uniformly distributed on [0, 1]. The valuations of the two
bidders are independent. Each bidder knows her own valuation, but not the valuation of
the other bidder. The bidders simultaneously submit bids b = [0, ∞), and whoever submits
the higher bid wins the object and pays the average of the two bids. In case of a tie, each
bidder wins the object with probability 1/2 and again the winner pays the average of the two
bids. Find a Nash equilibrium of this game in which each bidder's strategy is linear in her
valuation.
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