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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 second-price auction formats. In a first-price 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 second-price auction it is a weakly dominant strategy to bid your value, and hence expected revenue is simply the expected value of the second-highest 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