Leaders of the world’s largest and most dynamic economies will gather this weekend for what should have been simply another yearly summit.

But this annual gathering of 21 Asia-Pacific nations – whose members range from Thailand to China to Japan to the United States – comes at a time of strong pressure on them to resort to an old idea – namely, that prosperity and power only come at the expense of others.

This myth of limited good in human affairs is a hard one to break. But consider these challenges now facing the nations of the Asia-Pacific Economic Cooperation (APEC) forum:

At least seven Asian nations are clashing dangerously over claims to islands and the ocean resources around them. China and the US are beefing up their militaries in a contest for influence. And two proposals for regional trade pacts – one led by China, the other by the US – are competing for support.

In addition, slow growth in Europe, India, Japan, the US, and China has more nations scrambling for advantage in trade, resources, and commercial ideas. The very openness that made the Asia-Pacific region so dynamic is in jeopardy.

One reason behind these problems is that China regards the US as a superpower in decline, especially since the 2008 financial crisis. Its aggressive expansion in Asia has prompted the Obama administration to seek strong trade and military ties in the region, even with old foe Vietnam.

All sides in APEC still talk of “win-win” strategies. In fact, the theme of this year’s summit, which is being held in the Russian port city of Vladivostok, is “Integrate to Grow, Innovate to Prosper.”

But the recent challenges and clashes in Asia point to a return of the idea that there is a fixed amount of wealth and prestige in the world. The old belief that the strong only feed off the weak and that the rich only gain by depleting the poor could dominate again.

American leadership in Asia has long tried to dispel such archaic notions of humanity – by keeping sea lanes open, by opening US borders to trade, by welcoming foreign students to American universities, and by encouraging democracy in Asia.

China was reminded of America’s historic influence on Thursday when the prime minister of Singapore, Lee Hsien Loong, spoke in Beijing at the training school of China’s Communist Party.

“Among China’s external relationships, none is more important than that with the US,” stated the leader of the small city-state in Southeast Asia. “This is the most important bilateral relationship for both parties, and for the entire world.”

“The US will remain the dominant superpower for the foreseeable future. It is currently facing some very difficult problems, but it is not a nation in decline.”

“The US is an enormously resilient and creative society, which attracts and absorbs talent from all over the world, including many from China and the rest of Asia.”

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And, Mr. Lee noted, eight Nobel Prize winners in science who are of Chinese descent are American citizens. “We should never underestimate the US’s capacity to reinvigorate and reinvent itself,” he said.

Other regions of the world have long looked to Asia as a model of growth. This APEC meeting needs to keep that inspiration alive by making sure the region doesn’t slip back into zero-sum power plays or the kind of commercial mercantilism that assumes others must fail for one to succeed. Progress in history has only come when nations see their own good in helping others prosper.