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American leader visits internationally have typically been an opportunity to display the power of the American nation on the international platform. Donald Trump's multi-day tour through East Asia, conversely, has been a show of the power of the leader – but also, at moments, of that influence's constraints.

The president's stops in Malaysia, Japan and South Korea over the span of the initial days were an display in catering to a at times mercurial American president. It was an recognition that Trump, with the signature of a hand, could enact duties and other measures that have the potential to harm the markets of export-oriented states.

His sit-down with Beijing's head Xi Jinping on Thursday, though, was something entirely different.

It was a encounter of peers on the world platform, where the stakes for each country – for their markets, for their international prestige, for the prosperity of their citizens – were enormous.

With China, the US leader may wave his authority, but such actions entail ramifications. They carry a cost.

• The US president praises 'impressive' meeting with the Chinese leader but no agreement finalized
• Xi and the US leader reach short-term ceasefire as China adopts strategic patience

For the opening segment, Trump's latest foray into world politics was smooth sailing.

Each destination was punctuated by a combination of standard economic talks – arrangements made under the pressure of Trump's "equivalent" duties – and individual concessions that at points verged on the deferential.

In the Malaysian stop, Trump obtained entry to key materials and made headway toward completing trade arrangements with south-east Asian nations. He also oversaw a treaty that should alleviate border tensions between Thailand and Cambodia – the kind of "peace deal" the American president loves to tout.

In Japan, the president's helicopter flew past a famous structure illuminated red, white and blue – with a summit in Trumpian gold.

Newly elected Prime Minister Sanai Takaichi outlined $550bn in Japanese investments in the America and offered the US leader a gift of a quarter-thousand sakura trees for America's 250th anniversary, and a sports gear and case that came from the late leader, the assassinated ex-leader who bonded with the president in his first term.

She also became the newest foreign leader to suggest the president for his long-sought international honor.

Keeping pace, the Korean government welcomed the president with cannons discharging a honor salute and a military band that performed the leader's song and the classic tune – the band tune that has become a presidential event anthem.

President Lee Jae Myung held an "award event" for Trump during which he presented the president his state's premier award and a copy of an ancient Korean dynastic crown.

Midday meal with the Korean leader included a "Peacemaker's Dessert" of gold-covered baked goods. Subsequently, the hosts provided the president vineyard wine at an intimate dinner in the president's recognition with half-dozen world leaders participating in the regional summit summit.

In the United States, Trump may be the subject of "Anti-Authority" demonstrations by Americans who oppose his limit-pushing increases of presidential power, but during his East Asia tour he was received as royalty.

And like the kings of old, the president came to the Korean nation seeking tribute – in the form of $200bn in cash payments, $twenty billion a year, from Korea to the United States, to be allocated at the discretion of the president's administration. Agreement on the details of those payments contributed to that the tax percentage on South Korean goods to the US would drop from a quarter to 15%.

The main event of Trump's Asian tour occurred in its final hours, nevertheless, as he sat down with Xi.

There, the authority balance between counterparts of the planet's biggest economic powers was decidedly distinct than the meetings Trump had with his foreign counterparts in earlier stops.

Not present were the usual ceremony and the pageantry. Without any military bands, no honour guards, without thoughtfully prepared menus celebrating bilateral friendship. By contrast, the both heads and their key staff positioned themselves across a large pale negotiating table in a plain military building just adjacent to the landing strip of the city of Busan's international airport.

It was perhaps a reflection of the major consequences that when Trump exchanged greetings with Xi in the Korean city, he appeared