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[Auctions and Reserve Prices] Consider a seller who m good. There are two potential buyers, each with a valu values, vi € {0,1,2}, each value occurring with an equa are independently drawn. The seller will offer the good using a second-price seal price of r20 that modifies the rules of the auction as below r, then neither bidder obtains the good and it g then the regular auction rules prevail. If only one bid is highest bid obtains the good and pays r to the seller. a. What is the expected revenue of the seller when r = h Is it still a weakly dominant strategy for each player

[Auctions and Reserve Prices] Consider a seller who m good. There are two potential buyers, each with a valu values, vi € {0,1,2}, each value occurring with an equa are independently drawn. The seller will offer the good using a second-price seal price of r20 that modifies the rules of the auction as below r, then neither bidder obtains the good and it g then the regular auction rules prevail. If only one bid is highest bid obtains the good and pays r to the seller. a. What is the expected revenue of the seller when r = h Is it still a weakly dominant strategy for each player

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.4: Total Differentials And Approximations
Problem 23E: Eastern Hemlock Ring shake, which is the separation of the wood between growth rings, is a serious...
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[Auctions and Reserve Prices] 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, vi E {0,1,2}, each value occurring with an equal probability of 1/3. The players' values are independently 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. As seen in class, if both bids are below r, then neither bidder obtains the good and it goes "poof"! If both bids are at or above r then the regular auction rules prevail. If only one bid is at or above r then that bidder with the highest bid obtains the good and pays r to the seller. a. What is the expected revenue of the seller when r = 0 (i.e., no reserve price)? b. Is it still a weakly dominant strategy for each player to bid his valuation when r > 0? What is the expected revenue of the seller when r = 1? c. What is the optimal reserve price r for the seller, and what is the optimal expected revenue of the seller? (You may assume r is an integer.)
Transcribed Image Text:[Auctions and Reserve Prices] 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, vi E {0,1,2}, each value occurring with an equal probability of 1/3. The players' values are independently 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. As seen in class, if both bids are below r, then neither bidder obtains the good and it goes "poof"! If both bids are at or above r then the regular auction rules prevail. If only one bid is at or above r then that bidder with the highest bid obtains the good and pays r to the seller. a. What is the expected revenue of the seller when r = 0 (i.e., no reserve price)? b. Is it still a weakly dominant strategy for each player to bid his valuation when r > 0? What is the expected revenue of the seller when r = 1? c. What is the optimal reserve price r for the seller, and what is the optimal expected revenue of the seller? (You may assume r is an integer.)
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