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Presidential journeys internationally have traditionally been an opportunity to showcase the strength of the US on the world stage. Donald Trump's five-day swing through East Asia, by contrast, has been a show of the authority of the president – but also, at moments, of that power's limitations.

The president's destinations in Malaysia, Japan and South Korea over the course of the first four days were an demonstration in catering to a occasionally mercurial president. It was an acknowledgement that the leader, with the signature of a pen, could enact taxes and additional actions that have the potential to devastate the economies of export-oriented nations.

His meeting with China's president Xi Jinping on the last day, however, was a completely different scenario.

It was a encounter of counterparts on the global stage, where the risks for the two powers – for their markets, for their world reputation, for the prosperity of their populations – were enormous.

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

• Trump hails 'remarkable' encounter with Xi but no trade deal reached
• The Chinese president and the US leader establish brief pause as Beijing pursues extended strategy

For the first four days, the president's latest entry into world politics was smooth sailing.

Each stop was punctuated by a mix of traditional trade negotiations – arrangements made under the threat of the president's "mutual" taxes – and special treatment that at points bordered on the subservient.

In the Malaysian stop, the president obtained entry to essential resources and made progress toward completing economic agreements with south-east Asian nations. He also oversaw a treaty that should reduce frontier issues between Thailand and Cambodia – the sort of "peace deal" the American president loves to highlight.

In Japan, Trump's helicopter soared near a famous structure displayed American colors – with a summit in golden.

Newly elected Head Sanai Takaichi detailed $550 billion in Tokyo's funding in the United States and presented the president a present of a quarter-thousand flowering trees for the United States' 250th anniversary, and a golf equipment and case that was owned by the late leader, the murdered former prime minister who connected with Trump in his first term.

She also became the latest foreign leader to propose the president for his much-desired international honor.

Matching the effort, South Korea greeted the president with guns firing a traditional greeting and a armed forces orchestra that performed the presidential anthem and YMCA – the Village People song that has become a Trump rally standard.

President Lee held an "honour ceremony" for Trump during which he awarded the American leader his state's premier award and a model of an ancient Korean dynastic crown.

Midday meal with Lee contained a "Conciliatory Treat" of gilded brownies. Afterward, the Koreans served Trump fine beverage at an private meal in Trump's honor with six world leaders participating in the regional summit conference.

In the US, Trump may be the focus of "No Kings" rallies by US citizens who reject his boundary-testing extensions of executive authority, but during his Asian visit he was received as monarchy.

And like the kings of ancient times, Trump came to the Korean nation requesting tribute – in the form of $200 billion in monetary contributions, $20bn a year, from Korea to the US, to be invested at the guidance of the president's government. Agreement on the details of those payments helped ensure that the duty level on Korean goods to the US would drop from 25% to 15%.

The primary focus of Trump's Asia trip took place in its last moments, though, as he sat down with Xi.

At that location, the authority balance between leaders of the planet's biggest economic powers was decidedly different than the meetings the president had with his foreign counterparts in previous days.

Not present were all the ceremony and the spectacle. Lacking military bands, without ceremonial troops, missing meticulously designed dining selections honoring bilateral friendship. Instead, the two leaders and their top aides were seated across a long white discussion surface in a unremarkable service structure just off the runway of the southern port's international airport.

It was likely a demonstration of the major consequences that when the president exchanged greetings with Xi in the southern port, he seemed