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US presidential trips abroad have typically been an opportunity to showcase the influence of the US on the global scene. The president's five-day trip through East Asia, by contrast, has been a demonstration of the authority of the leader – but also, at times, of that influence's limitations.

Trump's destinations in Malaysia, Japan and South Korea over the course of the opening phase were an demonstration in catering to a at times mercurial president. It was an acknowledgement that the leader, with the stroke of a hand, could enact tariffs and other measures that have the ability to devastate the economies of trade-reliant countries.

His meeting with Beijing's head Xi Jinping on Thursday, nevertheless, was a completely different scenario.

It was a session of peers on the global stage, where the risks for the two powers – for their financial health, for their world reputation, for the prosperity of their populations – were enormous.

With China, the US leader may use his authority, but those steps come with repercussions. They come with a price.

• Trump hails 'impressive' talks with Xi but no agreement reached
• The Chinese president and Trump find brief pause as China pursues extended strategy

For the initial phase, Trump's latest entry into international relations was successful.

Each stop was marked by a combination of standard trade negotiations – agreements made under the shadow of Trump's "reciprocal" taxes – and individual concessions that at points verged on the deferential.

In the Malaysian stop, the president gained rights to key materials and made headway toward finalizing commercial deals with south-east Asian nations. He also oversaw a pact that should alleviate frontier issues between Thailand and Cambodia – the sort of "peace deal" the American president loves to promote.

In the Japanese leg, Trump's official aircraft flew past a landmark tower lit American colors – with a peak in golden.

Recently chosen Leader Sanai Takaichi outlined $550bn in Japanese investments in the US and presented the president a present of a quarter-thousand sakura trees for the United States' semiquincentennial, and a sports gear and carrier that was owned by the late leader, the murdered former prime minister who bonded with the president in his previous administration.

She also became the latest international head to propose Trump for his highly-coveted peace award.

Matching the effort, the Korean government welcomed the president with artillery firing a traditional greeting and a armed forces orchestra that performed Hail to the Chief and YMCA – the Village People tune that has turned into a political gathering theme.

Head the Korean president held an "recognition ritual" for Trump during which he presented the American leader his nation's highest medal and a model of an ancient Korean dynastic crown.

Lunch with Lee featured a "Peacemaker's Dessert" of gold-encrusted baked goods. Afterward, the Koreans served the president premium vintage at an private meal in Trump's honor with six international heads participating in the Asia-Pacific Economic Conference summit.

In the America, the president may be the target of "Anti-Monarchy" protests by US citizens who oppose his authority-expanding extensions of presidential power, but during his East Asia tour he was handled as royalty.

And like the monarchs of ancient times, Trump came to South Korea demanding payment – in the form of $two hundred billion in cash payments, $twenty billion a annually, from Korea to the United States, to be invested at the guidance of the president's leadership. Agreement on the details of those payments contributed to that the duty level on South Korean goods to the United States would decrease from twenty-five percent to 15%.

The central moment of the president's Asia trip took place in its final hours, nevertheless, as he sat down with Xi.

At that location, the authority balance between leaders of the world's two largest economies was decidedly different than the exchanges Trump had with his overseas colleagues in previous days.

Absent were all the pageantry and the spectacle. No armed forces orchestras, without protocol units, missing meticulously designed meal plans marking shared goodwill. Instead, the pair of counterparts and their senior advisors were seated across a large pale negotiating table in a unremarkable service structure just near the airstrip of Busan's global terminal.

It was likely a demonstration of the major consequences that when Trump made contact with the Chinese leader in Busan, he looked