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Unformatted text preview: Expected Revenue Here we calculate the expected revenue under the efficient equilibrium bidding strategies for the first and secondprice auction formats. In a firstprice auction with F ( ) uniform on [0,100], the symmetric equilibrium bidding strategy has each bidder bid ( n 1) / n times their value. Hence, expected revenue is simply ( n 1) / n times the expected value of the highest value. I.e., Expected revenue is n 1 n E [ v (1) ] = n 1 n Z 100 vf (1) ( v ) dv = n 1 n Z 100 v nv n 1 100 n dv = ( n 1) Z 100 v n 100 n dv = ( n 1) 100 n v n +1 n + 1 100 Rod Garratt ECON 177: Auction Theory With Experiments In a secondprice auction it is a weakly dominant strategy to bid your value, and hence expected revenue is simply the expected value of the secondhighest value. In case where F ( ) is uniform on [0,100], E [ v (2) ] = Z 100 vf (2) ( v ) dv = Z 100 vn ( n 1)( v n 2 100 n 1 v n 1 100 n ) dv = n ( n 1) Z 100 ( v n 1 100 n 1 v n 100 n ) dv = n ( n...
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This note was uploaded on 12/26/2011 for the course ECON 177 taught by Professor Garratt during the Fall '09 term at UCSB.
 Fall '09
 GARRATT

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