There was something fitting about Greek Prime Minister George Papandreou’s reckless call for a referendum on the latest rescue package for his country. World leaders gathering in Cannes for a Group of 20 summit face stark realities. The global economy is faltering, and no country has assumed leadership in organizing recovery. There is a loss of control, a vacuum of power. Papandreou’s disruptive decision — now apparently withdrawn — symbolizes this larger erosion of collective purpose. The world economy is adrift.

We are moving from Globalization 1.0 to Globalization 2.0. In Globalization 1.0, countries benefited from expanded trade and worldwide technology transfers. From 1980 to 2010, global trade volumes grew fourfold. Countless millions were lifted from poverty; new middle classes arose in Asia and Latin America. In Globalization 2.0, the economic interconnections among countries are breeding instability and nationalistic rivalries.

Time was when the United States automatically assumed the leadership role. Beginning in 1948, the Marshall Plan provided Europe with the equivalent of $850 billion — needed desperately to buy food, raw materials and machinery — to recover from World War II. In the 1980s, the United States took the lead in defusing the Latin American debt crisis; in the late 1990s, it did the same with the Asian financial crisis. The architecture of the postwar global economy was largely a product of U.S. leadership.

But under President Obama — possibly no one else could have done differently — America’s capacity and desire to lead have flagged. The 2007-09 financial crisis, having started in the United States, discredited American ideas and competence. The sluggish economy, heavy government debts and constant partisan haggling sap the nation’s financial power and political will to aid others. The United States hasn’t much helped Europe with its debt problems.

Europe represents a fifth of world economic output, about equal with the United States. It might have filled the leadership void; of course, it hasn’t. Instead, Europe has aggravated global instability, struggling with its own anemic growth and indebtedness. Even before Papandreou temporarily torpedoed the latest debt package — intended to aid Greece and shield Spain and Italy from default — there were doubts whether it was large enough.

To protect Italy and Spain, Europe’s rescue fund (the European Financial Stability Facility, or EFSF) needs 2.5 trillion euros to 3 trillion euros (from $3.5 trillion to $4.2 trillion), Willem Buiter, Citigroup’s chief economist, wrote recently in the Financial Times. The higher figure is nearly seven times the EFSF’s existing size. Where will all that money come from? Probably not Europe. Even Germany isn’t wealthy enough to assume all that extra debt.

China is one obvious answer, along with other Asian nations and oil producers with huge foreign exchange reserves. (At last count, reserves totaled $3.2 trillion for China, $516 billion for Russia and $484 billion for Saudi Arabia.) They have a clear interest in helping Europe avoid a full-fledged debt and banking crisis. Europe is a major market for their products.

But China has resisted a larger role, which many Europeans also oppose. “It’s shocking,” Martine Aubry, head of France’s socialist party, said recently of one modest effort to raise Chinese money for debt relief. “The Europeans, by turning to the Chinese, are showing their weakness. How will Europe be able to ask China to stop undervaluing its currency?” Others ask: If China is Europe’s lender, how can Europe criticize China’s human rights policies? Good questions.

A world of increasingly interconnected economies requires greater cooperation. But everywhere there is a growing fragmentation of power and purpose. Of course, no one country or group of countries can engineer a global recovery; economics is not yet (and may never be) such a precise and potent discipline. But leaders can emphasize policies that encourage recovery and reject policies that retard it. Demonstrated leadership instills confidence that accelerates economic expansion. The Marshall Plan built confidence.

After Lehman Brothers’ failure in 2008, cooperation seemed to flourish. Countries saw it in their mutual interest to adopt “stimulus” packages of spending increases and tax cuts to prevent a deeper economic collapse. Since then, the tide has reversed.

Weak economies have made countries more protective. In 2012, the U.S. economy will grow only 1.8 percent and the euro area (the 17 countries using the euro) 0.3 percent, forecasts the Organization for Economic Cooperation and Development. High joblessness tempts unpopular leaders to make risky gestures that, regardless of international consequences, aim to improve their domestic standing. See Papandreou, above. Differing political systems and values frustrate cooperation. See China, above.

The danger is a slow slide into currency wars and protectionism. The United States and Europe are retrenching from too much debt. China and many developing countries pursue export-led growth. This seems a formula for rising strife and economic stagnation.