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ECOS2201-prelect09 - D E R E M E N S EAD E M MUTA T...

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S I D E R M E N S · E A D E M · M U T A T O University of Sydney ECOS2201 - Lecture 9 1
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Auctions Auctions are used to sell many objects; houses, wine, art, but are also used to buy or procure objects; government funded infrastructure, house renovations. Same analysis applies regardless of whether buying or selling. We concentrate on the selling of objects (or bidding to buy). 2
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An auction is a private-value auction if bidders know their value (willingness-to-pay) for the object for sale Implicit in this situation is that no bidder knows with certainty the value of other bidders The private-value assumption is most plausible when value is derived from consuming the object; a car auction 3
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An auction is a common-value auction if bidders know the the object has a common value, but are uncertain about what this value is The common-value assumption is most plausible when value is derived from a market price - it has resale value; a vintage car auction Often objects have both private and common-value components - a house auction 4
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PRIVATE VALUE AUCTIONS The English Auction In an English Auction (or open ascending price auction) the price starts low and is increased successively. At each increment a bidder “holds” the object; that bidder wins the object at that price if no other bidder will pay more House auctions in Australia take this general form 5
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If valuation of object is x and bid p and win, then make a surplus of x - p A private-value bidder in an English auction has a simple optimal strategy. Question: What is it? 6
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The bidder with the highest valuation wins the auction and pays the valuation of the second highest bidder. The surplus made by the winning bidder is their value minus the second highest bidder’s value 7
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Second Price Sealed Bid Auction A second price sealed-bid auction (a Vickrey auction) is an auction in which the winner is the bidder with the highest bid, but the winners pays the second highest bid. Each bidder’s bid is unknown to the other bidders as they are placed in sealed envelopes. It turns out that in this auction bidders bid their private-values. 8
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Suppose highest other bid (unknown to bidder) is B. Bidder 1 has private value of x 1 and wins auction if b 1 B and loses auction if b 1 < B . 9
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Suppose bidder 1 bids z 1 < x 1 rather than value. If x 1 > z 1 B bidder 1 still wins and surplus is x 1 - B. If B > x 1 > z 1 bidder 1 still loses. However, if x 1 > B > z 1 , then bidder 1 loses whereas if bid x 1 would have won and made positive surplus. Therefore, bidding less than x 1 can never increase profit but in some circumstances may reduce it.
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