Bid shopping is a common practice for many general contractors (GC). The GC puts sub trades out for bid and then plays the sub contractors against each other trying to get a better price, after the bid. Many states and municipalities curtail this practice by requiring a GC to list the subcontractors the GC plans on using. The GC then must use that subcontractor (some exceptions do apply) so the practice of post bid; bid shopping is reduced, if not eliminated. Bill H.R 1778 would require listing of subcontractors on Federal construction projects.
American Subcontractors Association website has a link to write your member of congress in support of the bill.