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American leader visits overseas have historically been an occasion to demonstrate the strength of the United States on the world stage. Trump's week-long swing through East Asia, conversely, has been a demonstration of the clout of Trump – but also, at times, of that influence's limitations.

The president's destinations in Malaysia, Japan and Korea over the span of the opening phase were an exercise in pleasing a occasionally mercurial American president. It was an admission that the president, with the stroke of a pen, could enact tariffs and further steps that have the capacity to damage the financial systems of export-oriented countries.

His sit-down with China's president Xi on the final day, nevertheless, was something entirely different.

It was a meeting of counterparts on the world platform, where the risks for both nations – for their financial health, for their international prestige, for the well-being of their people – were enormous.

With the Chinese, the president may use his pen, but these moves entail repercussions. They involve a toll.

• The US president describes 'amazing' meeting with the Chinese leader but no pact finalized
• Xi and the US leader find short-term ceasefire as China adopts strategic patience

For the opening segment, Trump's most recent entry into international relations was smooth sailing.

Each visit was punctuated by a mix of standard economic talks – deals made under the shadow of the president's "equivalent" duties – and individual concessions that at times bordered on the deferential.

In the Malaysian stop, Trump obtained access to critical minerals and made headway toward finalizing trade arrangements with south-east Asian nations. He also oversaw a pact that should ease frontier issues between Thailand and Cambodia – the kind of "truce" the president loves to promote.

In the Japanese leg, Trump's Marine One passed by a Tokyo Tower illuminated US flag colors – with a peak in golden.

Freshly appointed Head the Japanese leader described $half-trillion in Japan's financial commitments in the United States and offered the American president a present of 250 flowering trees for America's 250th birthday, and a golf club and bag that came from former Prime Minister Abe, the killed past head who connected with the president in his previous administration.

She also became the newest international head to propose Trump for his long-sought international honor.

Not to be outdone, Korea received the president with cannons discharging a traditional greeting and a armed forces orchestra that played the presidential anthem and the Village People song – the musical group tune that has become a presidential event anthem.

Head Lee Jae Myung held an "honour ceremony" for Trump during which he gave the US president his state's top honor and a replica of an traditional ruler's coronet.

Noon repast with Lee included a "Peacemaker's Dessert" of gold-encrusted baked goods. Later that day, the Koreans offered the president vineyard wine at an private meal in the president's honour with half-dozen world leaders present at the Asia-Pacific Economic Conference meeting.

In the US, the president may be the subject of "Anti-Monarchy" rallies by US citizens who reject his boundary-testing extensions of executive authority, but during his Asian tour he was treated like nobility.

And like the kings of ancient times, Trump visited the Korean nation requesting contribution – in the guise of $200bn in cash payments, $20bn a per year, from the host nation to the United States, to be invested at the direction of Trump's leadership. Agreement on the terms of those payments assisted in that the tariff rate on South Korean goods to the America would fall from a quarter to 15%.

The primary focus of Trump's Asian tour occurred in its last moments, however, as he encountered the Chinese leader.

There, the power dynamic between leaders of the global top two markets was markedly different than the meetings the president had with his overseas colleagues in prior visits.

Not present were the usual ceremony and the display. Lacking military bands, without protocol units, no meticulously designed menus honoring mutual national affection. Instead, the pair of counterparts and their top aides were seated across a large pale meeting furniture in a unremarkable military building just adjacent to the landing strip of the southern port's international airport.

It was possibly a demonstration of the significant risks that when Trump exchanged greetings with the Chinese leader in Busan, he appeared