A view of Christie’s in New York this month, with Willem de Kooning’s “Untitled XXV” at center rear. The work sold for $66.3 million against an estimate of $40 million. Credit Brian Harkin for The New York Times

It was difficult to escape a sense of unreality in Manhattan last week.

High in his eponymous 664-foot-high tower in Midtown, a real estate tycoon and erstwhile reality show host, having just been elected as the 45th president, was appointing members of his administration while protesters down below chanted their disapproval.

At the same time, the three big international auction houses were trying to persuade the superrich to buy some of the world’s most expensive art. By and large, they succeeded.

Sotheby’s, Christie’s and Phillips’s latest biannual series of evening auctions of Impressionist, modern and contemporary art, which finished last Thursday, raised a total of $1.1 billion with fees. Despite concerns about a cooling global economy, “Brexit” and fallout from the election of Donald J. Trump, the total was 20 percent higher than the $893.2 million achieved at the equivalent series in May (excluding a $78.1 million themed sale at Christie’s).

“Everyone has been in the dark about how the market would react to the craziness that has been going on in the outside world,” said David Nisinson, a private art dealer based in New York. “We’re not back to 2007, but this must have a positive effect,” he said about the success of the five evening auctions, which all registered selling rates of more than 80 percent.

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But all three auction houses, using contrasting strategies, did manage to coax onto the market significant paintings in the $20 million to $50 million range, and ensure they found buyers.

Phillips posted the most improved results. Its Wednesday evening auction of 20th-century and contemporary works raised $111.2 million, more than double the $46.6 million from the equivalent sale in May.

The auction house, privately owned by Mercury, a luxury retail group based in Russia, has recently made a number of high-profile hires, including Robert Manley, a former deputy chairman at Christie’s, and Cheyenne Westphal, Sotheby’s former worldwide head of contemporary art, who starts in March.

Phillips’s evening sale in New York included the 1963 Gerhard Richter photo-based painting “Düsenjäger.” Credit Phillips

These reinforcements, such as Mr. Manley, and their contacts, are now attracting blue-chip artworks, albeit with financial inducements. Phillips’s evening sale included the 1963 Gerhard Richter photo-based painting “Düsenjäger,” valued at $25 million to $35 million, from the collection of the Microsoft co-founder Paul Allen. This “Capitalist Realist” (as the East German painters called their Pop Art) painting of a fighter jet had been backed by a third-party guarantor, who bought it with a single bid of $25.6 million with fees.

Edward Dolman, the chairman and chief executive of Phillips, described the result of his sale as “a significant step up in a market that has contracted.”

But the auction houses’ reliance on third-party guarantees to source and sell big-ticket artworks, particularly at Phillips and Sotheby’s, does raise the question of how much that $25.6 million for the Richter represented a “true” market price.

Values can be inflated when auction houses offer competitive guarantees to secure major consignments. These guarantee can then be transferred to a third party, who will either buy a work at a sale, or be rewarded for their unsuccessful bidding. More recently, some third-party guarantors — called “irrevocable bidders” at Sotheby’s — have also been paid fees if they are the purchaser. These confidential arrangements, denoted by symbols in the catalog, can have the effect of deterring bidding in the salesroom.

“It’s a sold picture, with uplift if possible,” said Alan Hobart, director of the Pyms Gallery in London. “The price is arranged by the vendor and is normally high. It’s become very opaque,” added Mr. Hobart, who paid $8.45 million for Picasso’s unguaranteed 1951 bronze sculpture, “Tete de Femme,” at Sotheby’s Nov. 14 auction of Impressionist and modern art.

Bidders at Sotheby’s were similarly lukewarm when Edvard Munch’s 1902 Symbolist masterwork, “Girls on the Bridge,” was offered — with a third-party irrevocable bid — as the star of an otherwise relatively thin 42-lot Impressionist and modern auction. Estimated at a heady $50 million, this was bought for $54.5 million by the guarantor.

In the case of both the Richter and the Munch, the third-party buyer was also paid a fee by the auction house. Following an approach from Sotheby’s, the New York City Department of Consumer Affairs recommended in September that “net” prices reflecting buyer discounts should be published after such sales, and all three houses have complied. The buyer of the Richter received about $1.6 million from Phillips; the buyer of the Munch $2 million from Sotheby’s, according to post-auction calculations.

“The air has got quite thin at the top,” said Wendy Cromwell, an art adviser based in New York. “There used to be at least two bidders on most of the lots, but now there is usually only one. Guarantees do provide cover for the lots and give a sense of security. But what do the totals mean in terms of profit? We’re blind.”

Sotheby’s offering of 25 works from the New York collectors Steven and Anne Ames, dubbed “The Triumph of Painting,” was the prize consignment of the evening sales (a further 54 Ames works were offered on Friday during the day). Mr. Ames, a partner at the investment house Oppenheimer & Co., died in March. Guaranteed for $100 million, the collection, with its emphasis on big, instantly recognizable paintings by bankable names such as Mr. Richter, Willem de Kooning, George Condo, Anselm Kiefer and Franz Kline, seemed to be exactly what the market ordered.

With 16 of the Ameses’ works covered by third-party “irrevocable” bids, competition was conspicuously measured. But a sumptuous red-hued 1986 Richter abstract, “A.B. Still,” which the Ameses bought at Sotheby’s in 1991 for $264,000, was doggedly pursued by two telephone bidders to a top price of $34 million, against an estimate of $20 million.

Over all, the 79 lots of the Ames Collection raised $131.3 million, a total which would suggest that Sotheby’s did make a profit on the guarantee.

Though Christie’s 61-lot auction of contemporary works on Tuesday night featured 17 guarantees, the most highly valued lot was offered free of financial encumbrances. Willem de Kooning’s much-admired 1977 abstract “Untitled XXV,” consigned by Bidzina Ivanishvili, the former prime minister of Georgia, according to Bloomberg News, soared to $66.3 million against an estimate of $40 million, an auction high.

Similarly, the following evening at Christie’s Impressionist and modern sale of 48 lots, Claude Monet’s 1891 “Grainstack” — a spectacular sunset from the artist’s first set of series paintings, also offered without a guarantee — set off a 14-minute bidding duel that ended in a telephone buyer paying $81.4 million with fees, also an auction high for the artist and the highest auction price this year.

Christie’s and Sotheby’s, the historic rivals of the auction world, are taking different approaches to winning consignments. The privately owned Christie’s has drawn back from the high-rolling guarantees that bought it market dominance in 2015 and is now luring sellers with the promise of higher prices in competitive bidding at its auctions.

The publicly traded Sotheby’s, particularly since its acquisition in January of the finance-oriented advisory company Art Agency, Partners, has favored presale guarantees as a means of capturing business, giving sellers the security of money on the table.

With Phillips now in the mix, three-way bidding for consignments of blue-chip works is becoming the new reality at the top end of the auction market. This is good news for owners of valuable art, if not bidders in salesrooms.

“I’m very happy, said a smiling François Odermatt, a collector based in Montreal, just before Phillips’s auction last Wednesday. “The more competition the better.”

Correction: November 23, 2016 

An earlier version of the article mischaracterized the status of Cheyenne Westphal at Phillips. She will take up a position there in March; she has not already joined the company.