Christie's had expected to sell the sculpture for $130 million and the Picasso for $140 million. Until this week, the most expensive work to sell at auction had been Francis Bacon's triptych of the artist Lucian Freud, which went for $142.4 million in 2013.
Paintings are fetching even higher prices away from the auction houses. A portrait of two Tahitian women painted by Paul Gauguin in 1892 sold privately for almost $300 million earlier this year, according to The New York Times. That was apparently the most anyone has ever paid for a work of art.
Figures like these will certainly raise eyebrows, especially at a time when investors worldwide have jitters about high prices in stocks, bonds and other assets. Some art collectors may be remembering the market's last contraction, which began in 1989 and lasted several years. Prices took more than a decade to recover.
"Is the art market now in a bubble? Is the bubble about to burst?" the economist Nouriel Roubini, who famously predicted the financial crisis of 2008, wrote in a note to investors earlier this year. "These questions are now being raised about the art market."
They are difficult to answer. A work or art isn't like a bond or a share of stock. It doesn't have a yield or a price-to-earnings ratio. There is no hard way of measuring how much it's worth. As a result, art is vulnerable to "fads, fashions, manias -- and potentially bubbles," as Roubini wrote.
Yet there are other explanations for the vast sums these works have been fetching. Art appeals to an ever larger class of the world's very rich, who may be hesitant to put their significant wealth in more conventional assets given lingering uncertainty about the health of the global economy and rapid swings in global currency values.
Economists debate whether art is a sensible investment. It generates similar returns to stock markets over the long term, according to Michael Moses, one of two experts behind the widely cited, proprietary Mei Moses family of art-market indexes. There have also been periods when art has yielded poor returns, though, particularly over the past 20 years, when stocks have done much better.
The price that people will pay to appreciate a fine painting in their homes, or simply to schmooze at galleries and fairs with talented and creative types along with well-heeled patrons like themselves, may be high enough to deter investors who don't enjoy these aspects of collecting.
"I don't think you should be investing in art purely for investment purposes," said Kathryn Graddy, an economist at Brandeis University. "You've got to like art."
There are a few reasons that anyone investing in art might be nervous at the moment, thinking back to the last big crash.
At a May 1990 auction, Christie's set a new record by selling a Vincent van Gogh for $82.5 million, including the commission. But with buyers paying less than the auctioneers' estimates for many other paintings, it was clear that prices were on the way down. Moses's index peaked that year, after several consecutive years of double-digit returns.
"After a string of returns like that, the markets in general will correct," Moses said.
During that correction, now more than 25 years ago, newly wealthy Japanese collectors were forced out of the market for art when the country's long period of economic growth gave way to a persistent slump.
With China now prospering as Japan did before, some art dealers today might be concerned about China's prospects for sustained growth. An economic crisis in China would mean fewer bidders at auctions worldwide, and particularly for the traditional Chinese works popular with the country's upper class and that have had particularly good returns in recent years.
Moses is less worried. He argues that global wealth is more widely spread around the globe than it was in 1990, and the art market is less dependent on any one nation's economy.
Also, prices haven't been rising for the past several years, in contrast to the last episode. Prices for art fell 22 percent in 2009 and have remained stable since then as investors have bet their money instead on a rapidly recovering stock market, Moses said.
Now, many investors are worried that equity market prices, which are already historically high, aren't likely to go up further -- a fear that was demonstrated last week when a comment by Janet Yellen led to a momentary sell-off.
"Equity-market valuations at this point generally are quite high," the head of the Federal Reserve said.
The price of art does not rise and fall with prices in the stock market, making it attractive to those who think stocks could lose value.
Investors worldwide have been seeking safe bets for years, bidding up prices for German bonds and land in London. For a sophisticated investor who makes careful purchases, art offers another kind of sanctuary. Even if Picasso, Giacometti and van Gogh generate only mediocre returns in the short term, their work has already stood up to the judgment of history, and is likely to retain its value for generations.
"Does it outperform inflation? Certainly," Moses said. "Is it a wealth preserver? Yes."
Andrew Shirley, who compiles Knight Frank's luxury-markets index, compared art to the world's most sought-after real estate. The supply is constrained, especially when it comes to provenance, and the demand is not.
"At the end of the day, it's not that complicated," Shirley said. "There are a limited number of these works of art, and an increasing number of very rich people who'd like to own them."
That fact could account for the exceptional performance of another sector of the art market: works priced over $10 million.
These masterpieces have been selling fast, in contrast to more modestly priced works. In other words, the art market appears to be polarizing between an extremely wealthy group of buyers who are paying ever higher prices for pieces like the Women of Algiers, and those who aren't rich enough to afford them.
In this way, the market for art resembles the one for consumer products more than the stock market. In groceries, clothing and more, vendors who cater to a smaller, wealthier group of customers have been more successful. Perhaps art dealers are also rushing to satisfy a clientele with the means to be more discerning in their demands.
"If you're rich and you've got a lovely house, you need to have nice things to hang on the wall," Shirley said.