Washington ? U.S. officials describe a common frustration in dealing with China over the past decade. Beijing wants to be recognized as a rising economic power but refuses to be an active partner in maintaining security. Beijing has seemed to want a free ride, without the corresponding responsibilities.

The next week will test whether China’s new president, Xi Jinping, intends to play a more engaged role with America and the world. Xi will spend two days in secluded strategic talks with President Obama, in what Chinese officials have been describing over the past year as a search for “a new type of great power relationship.”

The dilemma of great power relations that Xi and Obama will explore is often likened to the anxiety that the rise of Athens provoked in Sparta. As Harvard professor Joseph Nye noted back in 2005, the Peloponnesian War resulted from Sparta’s fears of an economically powerful Athens, but conflict wasn’t inevitable. It could have been averted by negotiations and wise policy. So, too, with America and China.

In the run-up to the meeting that will begin Friday at the Sunnylands estate east of Los Angeles, Xi offered a demonstration of China’s new stance. He bluntly warned a North Korean emissary in May that Pyongyang should back away from its reckless nuclear threats and negotiate peace with China, the U.S. and others. “The denuclearization of the Korean peninsula … is what the people want and also the trend of the times,” Xi said.

U.S. officials think the Chinese stopped waffling on North Korea for three reasons: They fear that a nuclear North Korea will force neighboring South Korea and Japan to have nuclear weapons, too; they worry that North Korea will proliferate technology to rogue nations and terrorists; and, perhaps most important, they fear the U.S. will take military actions to protect itself that will reduce China’s security.

If the Chinese become a more reliable, stand-up regional power, what do they get in return? That surely will be on top of Xi’s list of questions for Obama. The most dangerous test is a small chain of islands in the East China Sea that the Chinese call the Diaoyu and the Japanese the Senkaku. The Japanese have recently asserted a stronger claim of sovereignty over the islands and the Chinese have pushed back with gunboat diplomacy. The U.S. wants the issue to go away — taking no position on sovereignty and urging de-escalation — but it could be compelled by its defense treaty with Japan. It’s enough for now that Xi and Obama talk honestly about the issue.

The Chinese also want a partnership in managing the global economy. Vice Premier Wang Yang told visiting national security adviser Thomas Donilon last week that the two nations should “strengthen macroeconomic policy coordination, and jointly promote world economic recovery and growth.”

Beijing has come a long way from its skepticism during the depth of the Great Recession, when American capitalism seemed like the god that had failed. In a speech at the 2009 World Economic Forum in Davos, then-Prime Minister Wen Jiabao chided “inappropriate macroeconomic policies” and greedy banks, and called the American model “unsustainable.” The Chinese have changed their tune, thanks to solid economic measures by the Obama administration. Now they want even more free-market policies, on the American model.

The toughest nut will be cyber issues. Here, Chinese behavior has been egregious, stealing hundreds of billions of dollars’ worth of U.S. technology over the last decade, including many of the most secret U.S. weapons systems. Donilon said in March that the U.S. wants three things: a Chinese recognition that this is a real and urgent problem; a Chinese commitment to investigate; and agreement to cooperate on a framework for cyber protection. That will be the agenda at Sunnylands, but U.S. officials say they are looking for a strategic discussion rather than a “deliverable.”

The U.S.-China relationship is the biggest play on the board of international relations. This is an area where Donilon’s hyper-organized approach, which sometimes annoys his colleagues, has paid dividends. The U.S. has been building the groundwork for a new relationship with Xi for more than a year, and Donilon rightly says it could be Obama’s “signature achievement.”

U.S. officials stress in every speech about China the paramount need for military-to-military dialogue. Perhaps history would have been different if Spartan and Athenian commanders had been friendly, though I’m not sure. But given the stakes, this week’s summit meeting between Obama and Xi actually deserves the term “historic.”