Consider a seller who must sell a single private value good. There are two potential buyers,...

 

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Consider a seller who must sell a single private value good. There are two potential buyers, each with a valuation that can take on one of three values, v; € {0,1,2), each value occurring with an equal probability of. The players' values are inde- pendently drawn. The seller will offer the good using a second-price sealed-bid auction, but he can set a reserve price of r> 0 that modifies the rules of the auction as follows. If both bids are below r then neither bidder obtains the good and it is destroyed. If both bids are at or above r then the regular rules of the second-price auction prevail. If only one bid is at or abover then that bidder obtains the good and pays r to the seller. (a) Is it still a weakly dominant strategy for each player to bid her valuation when r > 0? (b) What is the expected revenue of the seller when r = 0 (no reserve price)? (c) What is the expected revenue of the seller when r = 1? Compare your answer to part (b). Consider a seller who must sell a single private value good. There are two potential buyers, each with a valuation that can take on one of three values, v; € {0,1,2), each value occurring with an equal probability of. The players' values are inde- pendently drawn. The seller will offer the good using a second-price sealed-bid auction, but he can set a reserve price of r> 0 that modifies the rules of the auction as follows. If both bids are below r then neither bidder obtains the good and it is destroyed. If both bids are at or above r then the regular rules of the second-price auction prevail. If only one bid is at or abover then that bidder obtains the good and pays r to the seller. (a) Is it still a weakly dominant strategy for each player to bid her valuation when r > 0? (b) What is the expected revenue of the seller when r = 0 (no reserve price)? (c) What is the expected revenue of the seller when r = 1? Compare your answer to part (b).

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SOLUTION a When the reserve price is greater than zero it is not a weakly dominant strategy for each ... View the full answer