What do you take "buy over our head" to mean in the following context?

Question

(Auction sale of the wreck of the "Flying Scud" in San Francisco)

. . . The auction will take place in the Merchants' Exchange at ten o'clock. . . . (Loudon to Pinkerton) "You seem to me to forget one trifle," said I. "Before you pick that wreck, you've to got to buy her, and how much will it cost?" "One hundred dollars, " replied Jim, with the promptitude of an automaton. "How on earth do you guess that?" I cried. "I don't guess; I know it," answered the Commercial Force. . . . How do you suppose I bought the James L. Moody for two hundred and fitfty, her boats alone worth four times the money? Because my name stood first in the list. Well, it stands there again; I have the naming of the figure, and I name a small one because of the distance (Midway Atoll); but it wouldn't matter what I named; that would be the price." "It sounds mysterious enough," said I. "Is this public auction conducted in a subterranean vault? . . ." "Oh, everything's open and above board!" he cried, indignantly. "Anybody can come, only nobody bids against us; and if he did, he would get frozen out. It's been tried before now, and once was enough. We hold the plant; we've got the connection; we can afford to go higher than any outsider; there's two million dollars in the ring; and we stick at nothing. Or suppose anybody did buy over our head - I tell you, Loudon, he would think this town gone crazy; he could no more get business through on the city front than I can dance; schooners, divers, men - all he wanted - the prices would fly right up and strike him." "But how did you get in (that ring)?" I asked. "You were once an outsider like your neighbours . . .?"

(The Wrecker by R. L. Stevenson and L. Osbourne, chapter ix, The Wreck Of The "Flying Scud" , published 1892)

Answer 1

• To bid more than someone at an auction, and therefore 'win' (secure) the goods offered for sale, in this case the wreck of a ship.

This idiom has been asked about before on ELL. But the specific meaning in the context cited here isn't covered by answers there. The speaker is (somewhat arrogantly) assuming that his company has the right to buy the boat. With the implication that no-one else should buy it without their permission/knowledge, which would not be granted. Effectively, anyone who outbid them would be "bypassing the proper authority" (the speaker's company), who are the only ones entitled to say who can or can't buy the boat (and they want it! :)

I think the speaker feels he wields the economic power more than has the right to set the price. And anyone who might outbid him would unleash a wave of price inflation from all of the other subcontractors ("schooners, divers, men") who would all raise their prices on the belief the winning bidder is able to bear a higher price. The higher bidder would not be able to "get business through on the city front".

_{(comment answers by Michael H and FF and TimR)}