This paper draws a remarkably simple bridge between auction theory and incentive theory. It considers the auctioning of an indivisible project among several fi rms. The firms have private information about their future cost at th e bidding stage, and the selected firm ex post invests in cost reduct ion. The authors show that (1) the optimal auction can be implemented by a dominant strategy auction that uses information about both the first bid and the second bid; (2) the winner faces a (linear) incenti ve contract; (3) the fixed transfer to the winner decreases with his announced expected cost and increases with the second lowest announce d expected cost; and (4) the share of cost overruns borne by the winn er decreases with the winner's announced expected cost. Copyright 1987 by University of Chicago Press.