Chinese President Xi Jinping (1st R) meets with U.S. President Barack Obama (1st L) at the Annenberg Retreat, California, the United States, June 7, 2013. Xi Jinping and his U.S. counterpart, Barack Obama, met Friday to exchange views on major issues of common concern. [Lan Hongguang/Xinhua]

The eyes of the world are on Sunnylands, a California ranch also known as the "Camp David of the West," where leaders of two of the globe's most important countries are having a historic meeting that could affect the future of mankind.

Officials and groups on both sides vie with each other to put their issue(s) on the agenda. President Xi Jinping and President Barack Obama will certainly discuss some of the major issues, but they probably will not be mired in arguing over specifics because they are confronted with the overarching challenge of how to avoid the "Thucydides trap."

Thucydides wrote in "The History of the Peloponnesian War," "The growth of the power of Athens, and the alarm which this inspired in Lacedaemon, made war inevitable." That war was not just caused by Sparta's fear of Athens' power; Corinth also blamed Athens for breaking a treaty in aiding Corcyra. Therefore there was also the danger of entangling alliances.

Research by a group of Chinese scholars shows there were seven times when a rising power challenged an established power since 1500, six of which eventually led to confrontation or war.

China's rise has been dramatic. Does the U.S. feel threatened? Projection by that group of Chinese scholars shows China will surpass the United States in terms of GDP by 2020, when China's GDP will be US$22.69 trillion, 3 percent higher than the U.S. GDP. Both the International Economic Review (2013, No.3) and the U.S. National Intelligence Council's "Global Trends 2030" predict that "China will probably have the largest economy, surpassing that of the United States a few years before 2030."

Is that why the Obama administration is rebalancing towards the Asia-Pacific? China will certainly play a bigger role in world affairs, yet it has no intention to challenge the U.S. Those scholars mentioned above advocate "a single order, multi-polar world and participatory governance." China needs to participate and maintain a single world order dominated by the U.S. It does not want to overturn that world order, because it is a beneficiary of that order. It only wants to reform those parts of the world order, which are unfair to developing countries. And what it proposes are incremental reforms, not fundamental changes.

When Xi Jinping visited the U.S. last year as China's Vice President, he called for a "new type of great power relations" that would set an example of constructive and cooperative relations for countries with different political systems, historical and cultural backgrounds and economic development levels; an example that is unprecedented and inspires posterity. He will certainly explore with Barack Obama at Annenberg's ranch ways to make that aspiration a reality.

What he meant by a new-type great power relationship can be summarized as cooperation, not confrontation; win-win results not a zero-sum game; and healthy competition, not spiteful rivalry.

We have reason to be optimistic as both China and the United States appear clear-eyed on the consequences of getting this relationship wrong.

Americans have been impressed by President Xi's self-confidence and no nonsense approach. Let us now hope that he and President Obama will take advantage of the "shirt-sleeves summit," dispensing with diplomatic formalities, and get down to the basics, build up mutual trust and establish a friendly personal relationship, so they will be better able to escape the "Thucydides trap."

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