To bid less than, as when a contract or service is offered to the lowest bidder; to offer to contract, sell, or do for a lower price than. [1913 Webster]
underbid, v. & n.
--v.tr. (-bidding; past and past part. -bid)
1 make a lower bid than (a person).
2 (also absol.) Bridge etc. bid less on (one's hand) than its strength warrants.
--n.
1 such a bid.
2 the act or an instance of underbidding.