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President Obama's trip to China yielded precious little Chinese cooperation on the Administration's key concerns, ranging from currency issues to Iran. That's a sign of the shifting balance of power between two countries that have been locked in an uneasy embrace for more than three decades. "I underlined to President Obama that given our differences in national conditions, it is only normal that our two sides may disagree on some issues," said China's President Hu Jintao. "What is important is to respect and accommodate each other's core interests and major concerns."

China's concerns, of course, have dramatically expanded in recent years, as was emphasized by Beijing's anxiety over the implication for its own dollar-denominated wealth of U.S. budget deficits. At the same time, Beijing is in no hurry to play the "other" global superpower rule vacated by the Soviet Union two decades ago.

Herewith, three key lessons to draw from the visit:

1. China's Star Has Risen and America's Has Ebbed, But the U.S. is 'Too Big to Fail'
As the Washington Post noted, when Bill Clinton visited Beijing a decade ago, the U.S. owed more money to Spain than it did to China. President Obama's America owes China some $800 billion and counting. China's economy is humming again, while America's is likely to remain sluggish for years. The sharp economic downturn, and the failure of the U.S. to impose its will in two very costly ongoing wars in Iraq and Afghanistan, have shrunk America's global leverage. Today, far less powerful countries than China routinely decline to follow Washington's lead. An ironic dividend of capitalism's Cold War triumph has been the emergence of new power centers in the world economy — Brazil, Russia, India and, of course, China.
Given its economic health and growing influence, Beijing is not simply able to rebuff U.S. demands; it is making its own demands of the U.S., in whose economy much of China's own wealth is tied up. For example, U.S. officials traveling with President Obama faced detailed questions about how the U.S. planned to pay for health-care reform, with China increasingly alarmed at the ballooning deficit and the gloomy economic outlook. The best thing going for the U.S. in its economic relationship with Beijing — which holds $800 billion in U.S. debt and some $2 trillion in dollar-denominated assets — is that for China, the American economy is simply "too big to fail".
While the U.S. currently needs Chinese help on a raft of economic and geopolitical issues, Beijing is less dependent on U.S. help, although it balks at any hint out of Washington of protectionist trade policies. While some in Washington will criticize Obama for being too deferential and allowing the Chinese to stage-manage the visit to avoid any domestic discomfort, it is the shift in the real balance of power that has forced the U.S. to change its approach to China.

2. China Doesn't Want to Run the World, But It Has Interests That Differ from America's
Russia may be engaged in a geopolitical chess game with the U.S. aimed at recovering from the demise of its great power status, but China is different. It pushes back against U.S. initiatives only when those are deemed inimical to its national interests. Iran is a good example. Beijing's heavy investment in and reliance on Iran's energy sector make it extremely averse to serious sanctions or strategies that create political turmoil in Tehran. While insisting on compliance with the non-proliferation regime, Beijing does not believe Iran represents an imminent nuclear weapons threat. And its response to North Korea going nuclear suggests that a nuclear armed Iran is something it could live with.
Obama went to China arguing that its emergence as a major power gives it greater responsibility, as a partner to the U.S., in helping run the world and tackle such global challenges as climate change and Iran. Indeed, there was a collective shudder in Europe's corridors of power at the idea of global leadership being concentrated in a "G2" partnership between Washington and Beijing. They needn't have worried. China's response to Obama could be read as: "Running the world is your gig, we're focused on running our own country, and ensuring security in our immediate neighborhood. We want harmonious relations with you, but don't expect us to do anything that we deem harmful to our national interests." That means no serious sanctions against Iran, regardless of what deals are struck between Washington and Moscow, because China's national interests require growing Iran's energy exports.

3. Personal Chemistry Can't Change the World
The personal trust between President Ronald Reagan and Soviet leader Mikhail Gorbachev was indispensable in fostering the climate for a rapid, peaceful end to the Cold War. Presidents Clinton, Bush and now Obama have all tried to cultivate personal relationships with their Chinese counterparts in the hope of smoothing a tricky relationship. But the usefulness of personal chemistry in dealing with China has strict limits, for a simple reason: While the President of the United States is, in George W. Bush's words, "the decider," his Chinese counterpart is not. He's not a figurehead, but executive power in Beijing is the preserve of a collective leadership in the form of the nine-man standing committee of the Politburo of the Chinese Communist Party — in which Hu is obviously the key player. Some observers say this is why the Chinese try to avoid informal one-on-one meetings with their U.S. counterparts, preferring more formal exchanges of talking points cleared with the Politburo. The problem of dealing with opaque foreign leadership structures is a recurring one for the Administration. Obama met with Russia's President Dmitry Medvedev last week to discuss sanctions against Iran, but nothing will happen unless Prime Minister Vladimir Putin is on board. And the Iranians themselves are even more complicated since the traditional balance of power between the government and the clerical leadership has been shaken up by the post-election turmoil. President Obama's personal charm and charisma may be a national asset when dealing with many countries, but, through no fault of his own, China is not necessarily one of them.

• Tony Karon