In November, 1975, the world’s leading industrial powers were staggering through a crisis beyond their control: The price of oil had more than quadrupled since OPEC imposed an embargo two years earlier. In the United States, unemployment had doubled. In Japan, the economy was shrinking for the first time since the Second World War. Communism was sweeping through Greece and Spain. In desperation, leaders of six large democracies—the United States, Britain, Japan, West Germany, France, and Italy—resolved to meet at the Château de Rambouillet, a castle that had been Louis XIV’s hunting lodge. They worked with no charter, no rules for membership, and no powers of enforcement. The results were vague, but one of the most enthusiastic supporters of this gathering of nations was Henry Kissinger, who declared that it would “give their peoples the sense that they are masters of their destiny, that they are not subject to blind forces beyond their control.” They called themselves the Group of Six—or G6.

By 1999, it was the G8, having added Canada and Russia, and though it had been credited with raising alarms about threats including genocide in Kosovo, the forum was now dogged by protesters and pilloried as a “closed club of an obsolescent rich white plutocracy” and a “global hot tub party.” In his 2003 book, “The Age of Consent,” George Monbiot, the British writer and activist, wrote, “We are left to shout abuse, to hurl ourselves against the lines of police, to seek to smash the fences which stand between us and the decisions made on our behalf.”

And yet, for all the abuse heaped on the G-model, it may turn out that the only thing more unsettling than a cabal of politicians meeting behind closed doors is a cabal of politicians who can’t agree to meet at all. That’s what we can expect this week at Camp David, when it’s America’s turn to host the G8. With urgent negotiations pending on Iran and Syria, the meeting has been undermined before it begins by Vladimir Putin’s decision to stay home, the first time a Russian President has done so. (The Kremlin said Putin could make better use of his time by finalizing his cabinet appointments.) Other forums for global leadership are ailing as well. The G20, which was created to make room for China, India, and other rising powers, helped stem the damage from the 2008 financial crisis, but subsequent meetings have yielded little, and the group is so sharply divided over basic political and economic values that summits have descended, in the view of the political scientist Ian Bremmer, into a herding of cats—“together with animals that don’t like cats.”

In “Every Nation for Itself: Winners and Losers in a G-Zero World,” Bremmer, the president of the political-risk consultancy firm Eurasia Group, maps the present and future of a “world order in which no single country or durable alliance of countries can meet the challenges of global leadership.” Bremmer, who publishes articles and books at a pace with which some others tweet, is a non-partisan presence in the commentariat, known for his writings on how global emerging markets upset established political and corporate rhythms. A book dedicated to criticizing the G-format would be about as likely to encounter spirited opposition as a denunciation of the Department of Motor Vehicles. But Bremmer’s “G-Zero” has a larger target: that giant sucking sound in geopolitics, the power-vacuum created by the end of the Cold War, the weight of debt and deficits around the neck of the United States, and a cluster of new powers not yet prepared to police an open and stable international system. “For the first time in seven decades, we live in a world without global leadership,” Bremmer writes. The G-Zero may only last for a decade or so, but in that time, he warns, it will be “an incubator of catastrophe.”

This is not an uplifting book; it reads like the geopolitical equivalent of a virus movie, which means it’s unsettling precisely because it’s plausible. Here are some of the “problems without borders” that he envisions: an influenza epidemic ravages the globe because of poor coördination and national secrecy; North Korea implodes, setting off a fight over who will safeguard the nuclear program and care for refugees; terrorists bring down airplanes because countries no longer agree on uniform standards for screening passengers and cargo; wars rage over contested sources of increasingly scarce water and food.

If that all sounds a bit too much like political sci-fi, consider some recent attempts at international coöperation. Bremmer gives a brisk recounting of the climate summit in Copenhagen in December, 2009, which Gordon Brown had hailed as “the most important conference since the Second World War.” By the time it was over, China’s Premier had withdrawn in anger to his hotel suite and sent a midlevel diplomat to negotiate with President Obama; the President of the Maldives, Mohamed Nasheed, had demanded of China how it could ask his country to “go extinct”; and Hugo Chávez had called Obama the devil. The summit collapsed not only because the players came from increasingly divergent positions but also because none of them had the power to impose a solution. (Meanwhile, in the years since, little progress has been made in the fractious debate over whether countries in the developing world should be held to the same emissions standards as industrialized ones, and the U.S. still refuses to sign the Kyoto protocol.)

Bremmer, who road-tested the idea of the G-Zero last year in Foreign Affairs, in an essay co-authored with the economist Nouriel Roubini, has written or co-written four books in the past five years, including, most recently, “The End of the Free Market: Who Wins the War Between States and Corporations?” In this case, he says, “the G-Zero won’t last forever,” but while it exists he’s content to sort the winners and losers. He’s betting on countries and corporations that maintain the widest range of potential allies, including “pivot states”—Turkey, Mongolia, Brazil, and so on—that have maintained relations with a range of big powers. Losers, we’re told, will be those who depend too heavily on American protection—so long, Japan and Taiwan!—and “shadow states,” such as Mexico and Ukraine, which cling, suckerfish-like, to the fortunes of larger neighbors. Above all, the author is unsentimental. “Winners accept the world as it is,” he writes, and predicts that “banks, hedge funds, and private equity funds will shift their operations toward emerging-market states to avoid global and Western regulatory reforms.” If China’s new dominance in Africa arouses protests, there is “no reason why Western-based companies can’t exploit these vulnerabilities and compete more effectively with Chinese companies.”

In a G-Zero world, he concludes, “it is economic muscle, not military might, that determines the international balance of power.” But that view may understate some ingredients and overstate others. Take China. Despite signs of an economic slowdown in recent months, China’s government has more economic verve than any other major power, but this has failed to make up for its persistent deficit in diplomatic and political charm. For all of China’s market appeal and manufacturing power, it has lost out on some minor but telling measures of influence, such as the international adoption of China’s 3G phone standard or its version of Wi-Fi, called WAPI.