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Presidential journeys overseas have traditionally been an chance to demonstrate the influence of the American nation on the global scene. Donald Trump's week-long trip through Asian nations, by contrast, has been a show of the authority of Trump – but also, at moments, of that influence's limitations.

Trump's destinations in Malaysia, Japan and South Korea over the duration of the first four days were an exercise in pleasing a sometimes mercurial American president. It was an acknowledgement that the leader, with the flick of a document, could impose tariffs and other measures that have the potential to devastate the economies of trade-reliant nations.

His meeting with China's president Xi on Thursday, though, was a distinct situation.

It was a encounter of counterparts on the global stage, where the risks for both nations – for their markets, for their world reputation, for the welfare of their citizens – were significant.

With China, Trump may wave his authority, but such actions entail consequences. They carry a price.

• The US president describes 'amazing' talks with the Chinese leader but no trade deal agreed
• The Chinese president and the US leader reach brief pause as Beijing pursues extended strategy

For the first four days, the president's most recent foray into international relations was successful.

Each destination was characterized by a combination of conventional economic talks – deals made under the pressure of the president's "mutual" tariffs – and personal accommodations that at points approached the obsequious.

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

In the Japanese leg, the president's helicopter passed by a famous structure displayed red, white and blue – with a summit in gilded.

Recently chosen Leader Takaichi described $half-trillion in Japan's financial commitments in the US and gave the American president a present of 250 flowering trees for the United States' 250th anniversary, and a golf club and bag that came from former Prime Minister Abe, the killed ex-leader who developed ties with Trump in his previous administration.

She also became the most recent overseas counterpart to propose Trump for his long-sought Nobel Peace Prize.

Matching the effort, South Korea received the president with guns performing a honor salute and a military band that played the leader's song and the Village People song – the band anthem that has evolved into a political gathering anthem.

Leader Lee held an "award event" for Trump during which he gave the American leader his nation's top honor and a model of an traditional ruler's coronet.

Midday meal with the Korean leader featured a "Diplomat's Sweet" of gold-encrusted baked goods. Subsequently, the Koreans offered Trump fine beverage at an intimate dinner in the president's honor with six world leaders present at the Asia-Pacific Economic Conference conference.

In the US, the president may be the subject of "Anti-Authority" demonstrations by US citizens who oppose his authority-expanding extensions of presidential power, but during his Asian visit he was received as monarchy.

And like the rulers of ancient times, the president visited South Korea seeking tribute – in the form of $200bn in monetary contributions, $20 billion a year, from Korea to the United States, to be allocated at the direction of Trump's administration. Agreement on the details of those payments helped ensure that the tariff rate on host nation products to the America would drop from twenty-five percent to 15%.

The central moment of Trump's Asia trip occurred in its last moments, nevertheless, as he sat down with the Chinese leader.

There, the authority balance between leaders of the planet's biggest economic powers was noticeably divergent than the exchanges the president had with his foreign counterparts in prior visits.

Absent were all the ceremony and the spectacle. No service ensembles, without ceremonial troops, missing thoughtfully prepared menus celebrating mutual national affection. Instead, the two leaders and their top aides were seated across a extended light-colored negotiating table in a unremarkable service structure just off the runway of Busan's air transport hub.

It was perhaps a demonstration of the high stakes that when Trump exchanged greetings with the Chinese leader in Busan, he seemed