People who study the outcomes of auctions, such as where several firms propose to handle a block of matters over time have coined a memorable term for a notorious outcome: the “winner’s curse.” In most auctions, the winner is cursed by having paid more than the economically optimal amount. After all, no one else was willing to offer as much, so the winner has probably overpaid (See my post of Feb. 4, 2006 #4 on auctions and the references cited.).
One way to lessen the curse of the winner is to allow a second round of bidding after the first round. Disclose all the bids – not who bid them. Each bidder who remains then calibrates its bid amount against all the others and may adjust its bid. Another way is to select highest bidder, who pays the amount of the second highest bid.