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American leader visits overseas have historically been an chance to display the strength of the US on the international platform. Donald Trump's week-long swing through eastern Asia, on the other hand, has been a display of the authority of Trump – but also, at points, of that authority's limitations.

Trump's visits in Malaysia, Japan and South Korea over the course of the first four days were an exercise in catering to a occasionally volatile president. It was an recognition that the president, with the stroke of a document, could introduce tariffs and other measures that have the ability to harm the economies of trade-reliant states.

His sit-down with Beijing's head Xi Jinping on the final day, however, was a distinct situation.

It was a encounter of counterparts on the international scene, where the risks for each country – for their financial health, for their world reputation, for the well-being of their citizens – were significant.

With China, the president may use his authority, but such actions come with ramifications. They come with a cost.

• Trump hails 'amazing' meeting with Xi but no pact agreed
• The Chinese president and Trump find short-term ceasefire as Beijing pursues extended strategy

For the opening segment, the president's latest entry into world politics was uneventful.

Each visit was characterized by a mix of traditional economic talks – agreements made under the threat of the president's "mutual" taxes – and special treatment that at moments approached the obsequious.

In Malaysia, Trump secured rights to critical minerals and made advances toward concluding economic agreements with ASEAN countries. He also oversaw a agreement that should reduce frontier issues between Thailand and Cambodia – the sort of "truce" the US leader enjoys to highlight.

In the Japanese leg, the president's helicopter passed by a landmark tower lit US flag colors – with a top in Trumpian gold.

Newly elected Head the Japanese leader detailed $550 billion in Japanese investments in the US and presented the president a gift of a quarter-thousand sakura trees for the United States' 250th anniversary, and a sports gear and case that came from the late leader, the killed former prime minister who connected with Trump in his previous administration.

She also became the latest international head to propose the president for his highly-coveted international honor.

Keeping pace, the Korean government welcomed the president with guns discharging a 21-gun salute and a military band that rendered the leader's song and the classic tune – the musical group song that has turned into a presidential event standard.

Head the Korean president held an "recognition ritual" for the US leader during which he gave the American leader his country's premier award and a replica of an historical royal headpiece.

Noon repast with the Korean leader contained a "Diplomat's Sweet" of gilded brownies. Later that day, the Koreans served the president vineyard wine at an exclusive gathering in Trump's recognition with six international heads present at the regional summit meeting.

In the US, Trump may be the focus of "Anti-Authority" rallies by the public who oppose his authority-expanding extensions of executive authority, but during his regional tour he was received as nobility.

And like the rulers of history, the president arrived in the Korean nation requesting tribute – in the shape of $200bn in cash payments, $20 billion a per year, from the host nation to the America, to be used at the direction of the president's leadership. Approval on the terms of those transfers assisted in that the tax percentage on host nation goods to the US would fall from 25% to 15%.

The main event of the president's Asia trip came in its concluding phase, however, as he met with the Chinese leader.

There, the influence relationship between heads of the world's two largest economies was decidedly divergent than the interactions Trump had with his foreign counterparts in earlier stops.

Missing were all the pomp and the display. No service ensembles, no ceremonial troops, no carefully crafted menus celebrating bilateral friendship. By contrast, the two leaders and their senior advisors positioned themselves across a extended light-colored meeting furniture in a unremarkable armed forces facility just off the runway of Busan's air transport hub.

It was perhaps a reflection of the significant risks that when Trump exchanged greetings with Xi in the southern port, he looked