Many people, like my old friend Brad Glosserman, find it hard to understand why China is acting the way it is in the East and South China Seas. What does Beijing hope to achieve by alienating its neighbours and undermining regional stability?

Let me suggest an answer: China is trying to build what President Xi Jinping calls 'a new model of great power relations'. To understand how this might be the aim of Beijing's actions, we have to recognise that under his 'new model', Xi wants China to wield much more power and influence in Asia than it has for the past few centuries. These things are inherently zero-sum, so for China to have more power and influence, America must have less. This is what Xi and his colleagues are trying to achieve.

Their reasoning is simple enough. They know that America's position in Asia is built on its network of alliances and partnerships with many of China's neighbours. They believe that weakening these relationships is the easiest way to weaken US regional power. And they know that, beneath the flowery diplomatic phrases, the bedrock of these alliances and partnerships is the confidence America's Asian friends have that America is able and willing to protect them from China's power.

So the easiest way for Beijing to weaken Washington's power in Asia is to undermine this confidence. And the easiest way to do that is for Beijing to press those friends and allies hard on issues in which America's own interests are not immediately engaged – like a string of maritime disputes in which the US has no direct stake.

By using direct armed pressure in these disputes, China makes its neighbours more eager for US military support, and at the same time makes America less willing to give it, because of the clear risk of a direct US-China clash. In other words, by confronting America's friends with force, China confronts America with the choice between deserting its friends and fighting China. Beijing is betting that, faced with this choice, America will back off and leave its allies and friends unsupported. This will weaken America's alliances and partnerships, undermine US power in Asia, and enhance China's power.

This view of China's motives explains its recent conduct.

Ever since President Obama announced the 'pivot', China has tested US willingness to support its allies over the Scarborough Shoals and Senkaku/Daioyu disputes. Until his Asian trip last month, Obama seemed inclined to step back from America's commitments, but his bold words in Tokyo and Manila suggest he has recovered his resolve to stand firm.

Now we can expect China to test this newly-recovered resolve by applying more pressure in the same places or elsewhere. And that is what Beijing is doing today in the waters off Vietnam. It is calling Obama's bluff. Expect more pressure against Manila and Tokyo soon.

Of course this carries risks for China. It does not want to fight America, so it must be confident in the judgement that America will back down and desert its friends rather than engage in conflict with China, even if backing down badly weakens the US position in Asia. This confidence reflects two key judgments by China's leaders.

First, they believe that China's new anti-access/area denial capabilities can deny America a quick and easy victory in an maritime clash in the East Asian littoral waters. They have been reassured by America's own Air-Sea Battle doctrine that the US knows it cannot prevail in these waters without launching a major campaign of strikes against Chinese territory. Such strikes would obviously risk a major escalation which might not stop below the nuclear threshold. So China's leaders think their US counterparts understand that a war with China today is one that America could not be confident of either winning or limiting.

Second, Beijing believes the balance of resolve is on China's side. Washington clearly wants to preserve its role in Asia, but Beijing is even more determined to win power at US expense. China's conduct suggests that the leadership in Beijing believes Washington understands this imbalance of resolve. That makes the Chinese confident that US leaders will not assume that China would back down first in a crisis.

The idea that China might believe these things comes as a surprise to many outside China, including, one suspects, many in Washington. US policy towards China, including the pivot itself, is based on contrary assumptions. The consensus is that Beijing is not really serious about challenging US leadership in Asia because it is simply not willing to risk a confrontation with America which Beijing's leaders must know they would lose, and they do not care enough about expanding China's role in Asia to take that risk.

If that's true, then as Brad Glosserman says, China's conduct is clearly foolish. But before assuming that the Chinese leaders are fools, we would be wise to wonder whether they really do believe what Washington assumes they believe. I'm pretty sure they do not.

Asia today therefore carries the seeds of a truly catastrophic episode of mutual misperception. Both Washington and China are steadily upping the stakes in their rivalry as China's provocations of US friends and allies become more flagrant and America's commitments to support them become more categorical. Both believe they can do this with impunity because both believe the other will back down to avoid a clash. There is a disconcertingly high chance that they are both wrong. Someone needs to change the nature of the game to avert the risk of disaster.