Under contractual incompleteness, a bid-taker is obliged to depend on a self-enforcing contract where a winning bidder puts his reputation at stake. In this case the winning bidder will renege on contractual obligations if any one-shot gain from opportunism is greater than a long-term gain from maintaining his reputation. Since the long-term gain is decreasing in the number of competing bidders, excessive bidding competition may provoke the winning bidder's opportunism. We derive an optimum number of bidders which ensures the self-enforcing contract at the lowest expected procurement cost. We also show how excessive bidding competition leads to the phenomenon of cost overruns.