The bids spiraled higher and higher until -- bang! -- the hammer fell: sold, for $62.75 million.

A sense of relief rippled through Sotheby’s elegant Manhattan headquarters as “Untitled (New York City),” a celebrated painting by Cy Twombly, ultimately set an auction record for the artist.

For behind the heady gavel price was a hard business reality: even as the crowd sipped champagne that evening, Sotheby’s was still frantically wooing a buyer. In the end, the grand old auction house had to pay for the privilege of selling the masterpiece.

That’s pretty much how it goes in the auction business these days. Like many works of art, the 1968 “Untitled” was sold under what is politely known as the “enhanced hammer,” behind-the-scenes deals that are shifting the balance of power inside the notoriously opaque market for art.

Sotheby’s, like its chief rival, Christie’s, typically collects fees from buyers and sellers. While the houses have often waived seller commissions for showpieces, cut-throat competition has forced them to sweeten deals even more to lure hedge fund types and other deep-pocketed collectors.

Last-Minute Deal

When Sotheby’s auctioned off “Untitled” last November, it handed the seller, Los Angeles art patron Audrey Irmas, most of its $7.8 million buyer fee on top of the hammer price, according to people familiar with the matter. It also cut a risky deal with the buyer, hedge fund manager Daniel Sundheim.

The financial gymnastics say a lot about faded fortunes of the world’s two big auction houses. A decade and a half after the world learned the pair had colluded to rig seller commissions, the auction-house equivalent of a price war has broken out. The battle has grown so fierce that the houses are offering a range of incentives to win consignments, often at the expense of their own profits.

“They have been making absolutely absurd deals just to be seen selling this Koons or that Rothko,” said David Nash, co-owner of Mitchell-Innes & Nash, a gallery in New York, and a former Sotheby’s executive. “They’d do anything to get the deal away from the competition.”

Few in the auction trade will talk openly about specifics, but many agree these arrangements have become ubiquitous. Sotheby’s declined to comment on the Nov. 11 sale, as did Irmas and Sundheim.