2. Consider an auction for Elvis memorabilia. There are two bidders, i and j, with private...

 

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2. Consider an auction for Elvis memorabilia. There are two bidders, i and j, with private values who compete in a first-price auction. Each bidder knows his private value and believes the other bidder's private value is drawn from a uniform distribution on the interval [0, £6000] and this is common knowledge. (a) If bidder j is bidding half her valuation and bidder i bids half of w,,then show that bidder i's expected surplus is Wi (vi -1/2) 6000 Use this to show that it is an equilibrium to use the bid function b(v) = v. Now assume the bidders are of different types. Assume that Bidder 2 believes that bidder 1's valuation is drawn from the distribution Fi(v) which is uniform on the interval [0, £6000] as before. However, bidder 1 knows that bidder 2 is an Elvis fanatic and his valuation is drawn from the distribution F₂ (v) where F₂(v) < F₁ (v) for all u. In the lecture next week we will see that in equilibrium they will now use different bid functions B₁(v) and B₂ (v). (b) Explain why the outcome of this auction is not necessarily efficient. Intuitively, do you think bidder 1 will bid more or less than he did in part a) now that he knows that he is up against an Elvis fanatic? 2. Consider an auction for Elvis memorabilia. There are two bidders, i and j, with private values who compete in a first-price auction. Each bidder knows his private value and believes the other bidder's private value is drawn from a uniform distribution on the interval [0, £6000] and this is common knowledge. (a) If bidder j is bidding half her valuation and bidder i bids half of w,,then show that bidder i's expected surplus is Wi (vi -1/2) 6000 Use this to show that it is an equilibrium to use the bid function b(v) = v. Now assume the bidders are of different types. Assume that Bidder 2 believes that bidder 1's valuation is drawn from the distribution Fi(v) which is uniform on the interval [0, £6000] as before. However, bidder 1 knows that bidder 2 is an Elvis fanatic and his valuation is drawn from the distribution F₂ (v) where F₂(v) < F₁ (v) for all u. In the lecture next week we will see that in equilibrium they will now use different bid functions B₁(v) and B₂ (v). (b) Explain why the outcome of this auction is not necessarily efficient. Intuitively, do you think bidder 1 will bid more or less than he did in part a) now that he knows that he is up against an Elvis fanatic?

Answer rating: 100% (QA)

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