Consider a second-price sealed bid auction with n bidders. The player with

the highest bid obtains the object and pays a price equal to the second highest

bid. In case of a tie, each player obtains the object with probability m1 , where

m equals the number of bidders who share the highest bid. Player i's valuation

of the object is i [0; ]. The values 1 , ..., n are drawn independently from

a commonly known distribution on [0; ]. Bidder i knows i , but not j for

ji . Let p denote the price paid for the object. The payoff to player i is

i - p if he obtains the object

0 if he does not obtain the object.

Show that bidding truthfully, that is, bi (i ) =i weakly dominates bidding

an amount higher than i