During Vice President Joe Biden's visit to China, Beijing and Washington confined their brawling to the basketball court, and for now economic and political needs should keep tensions in the diplomatic arena from spiraling into fully-fledged feuds.

With some two thirds of their nation's $3.2 trillion of foreign exchange reserves in dollar assets, and their own tricky power handover to navigate, China's leaders used Biden's visit that ended on Monday to signal that, despite U.S. economic woes, they are not yet writing obituaries for American power.

Both Biden and his Chinese hosts showed they want to avoid unnerving blow-ups with global markets already spooked. Both governments also face a potentially volatile political season in 2012, when President Barack Obama runs for re-election and the Chinese Communist Party installs new leaders.

In China nowadays there's a variety of viewpoints. Some people see the United States as in decline, said Zhu Feng, a professor of international relations at Peking University who specializes in Sino-American relations.

But the Chinese leadership's view is that although the U.S. economy faces difficulties, it will improve ... I think this visit was deliberately arranged to send a clear signal that China does not see the United States in decline and believes it can overcome the current hardships.

The atmosphere of goodwill during Biden's visit was marred by a fight that broke out during a friendship basketball game in Beijing between Washington's Georgetown Hoyas and the Chinese side, the Bayi Military Rockets.

A senior Obama administration official accompanying Biden said there was clearly a shared understanding that with the upcoming leadership transitions figuring out how to manage the relationship was more complicated -- and a priority. The official spoke on condition of anonymity.

XI, WILL YOU BE MY G2?

Chinese Vice President Xi Jinping, who is virtually certain to succeed Hu Jintao as Chinese President in early 2013, hosted Biden during this visit.

Obama administration officials have said they want to build trust with Xi (pronounced Shee) ahead of the leadership transition and came away assured.

Clearly both of them will walk away from ... these few days with a much, much better understanding for the other guy, what's driving the other side, what is constraining the other side, said another U.S. official who accompanied Biden to Beijing and the southwest Chinese city of Chengdu.

Disputes from human rights to Taiwan to the South China Sea offer plenty of kindling for abrupt feuds, but several analysts and officials said that the two sides are unlikely to seek a scrap now.

For China, the most tricky issue is Taiwan, the self-ruled island that Beijing calls an illegitimate breakaway. Last year, China vehemently condemned the Obama administration for approving a package of arms sales to Taiwan.

The administration is considering another arms sale, but sources have told Reuters that any deal is unlikely to include new Lockheed Martin F-16 fighter jets, which Beijing has made the focus of its objections.

Biden gave an extra push to the notion that the two countries are an informal G2, a pair whose power sets them a rung above the other major powers in the G20 bloc and that cooperation would help the global economy.

I hope this doesn't sound chauvinistic to other countries, but our mutual success will benefit the whole world, Biden told senior officials in Beijing. It is the key, in my view, to global economic stability.

Tensions in the South China Sea, with the risk of military jostling, could also spark quarreling between China and the United States. But Andrew Small, a researcher at the German Marshall Fund think-tank in Brussels who studies Chinese foreign policy, said both sides hope to keep those disputes on the back-burner.

At one level you're getting more of this kind of G2 relationship, and a deal to restrain tensions, said Small. But simultaneously, there's still a lot of kicking and pushing under the table, especially in Asia-Pacific.

Still, Washington may believe the G2 talk encourages Beijing to be more accommodating in international dealings, an analyst said, but in China a widely shared sense of the nation's rising power also encourages views that Beijing should stand tougher.

A recent study by the Chinese Academy of Social Sciences showed that 45.9 percent of respondents said their government should stick more firmly to principles when dealing with the United States, while 41.3 percent said it should be a bit more flexible.

It's clear that even before this latest problem with the debt ceiling and the cascading debt problems in Europe, the Chinese were saying that the West has been damaged by the financial crisis and China is narrowing the gap, said Bonnie Glaser, an expert on U.S.-China ties at the Center for Strategic and International Studies, a think-tank in Washington D.C.

There are louder and louder voices that are saying ... the U.S. is increasingly weak and therefore China can stand up for its core interests, she said in an interview before Biden's visit.