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slide36-nov30 - ECON 401: Auction Siyang Xiong Rice...

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Unformatted text preview: ECON 401: Auction Siyang Xiong Rice University November 30, 2011 Xiong (Rice University) ECON 401 November 30, 2011 1 / 15 all-pay auction n bidders and bidders&values are i.i.d. distributed uniformly on [0,1]; the assumptions of revenue equivalence are satised. Hence, by previous notes, the expected payment of bidder 1 with value v 1 is m all & pay . v 1 / D Z t D v 1 t D g . t / tdt . where G . t / D [ F . t / ] n & 1 D . t / n & 1 and g . t / D dG . t / dt D . n & 1 / . t / n & 2 . Suppose b all & pay . / is the symmetric bidding equilibrium in the all-pay auction, i.e., bidder 1 with value v 1 should bid b all & pay . v 1 / . Then, what is the expected payment of bidder 1 with value v 1 ? - just b all & pay . v 1 / . Therefore, b all & pay . v 1 / D Z t D v 1 t D g . t / tdt D Z t D v 1 t D . n & 1 / . t / n & 2 tdt D & n & 1 n t n t D v 1 t D D n & 1 n . v 1 / n . Xiong (Rice University) ECON 401 November 30, 2011 2 / 15 all-pay auction: a second way bidder 1 could pretend he has value v 1 2 [ r , 1 ] and bids b & v 1 , and he gets the expected payo/: & v 1 n & 1 v 1 & b & v 1 if he bids b & v 1 , the probability he wins is: Pr & . v 2 , ..., v n / : b . v 2 / b & v 1 , b . v 3 / b & v 1 ,..., b . v n / b & v 1 D Pr & v 2 : v 2 v 1 ... Pr & v n : v n v 1 , because b . k / is increasing D F 2 & v 1 F 3 & v 1 ... F n & v 1 D F & v 1 n & 1 D & v 1 n & 1 if he wins, he gets the object, i.e., gets v 1 ; if he loses, he gets nothing; he pays a price of b I & v 1 , regardless of winning....
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This note was uploaded on 02/09/2012 for the course ECON 401 taught by Professor Siyang during the Spring '11 term at Rice.

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slide36-nov30 - ECON 401: Auction Siyang Xiong Rice...

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