Consider the case that the highest bid is strictly higher than the
second highest bid. In this case, for exactly one value of j,
will be non-zero. Some agent (possibly the
auctioneers) can collect the 
polynomials and determine
the winner. Since there can be only one bidder with a higher price,
this reveals no extra information.
If there is a tie for the highest bid, then 
, and for at least two values of j,
. These values of j correspond to the tied
bidders.