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US presidential trips overseas have typically been an occasion to demonstrate the power of the American nation on the world stage. Donald Trump's week-long swing through East Asia, conversely, has been a show of the power of Trump – but also, at points, of that influence's limitations.

Trump's stops in Malaysia, Japan and Korea over the course of the opening phase were an exercise in catering to a sometimes mercurial American president. It was an recognition that the leader, with the signature of a hand, could enact tariffs and other measures that have the capacity to damage the economies of export-dependent countries.

His discussion with Chinese leader Xi on Thursday, however, was a distinct situation.

It was a session of equals on the global stage, where the risks for both nations – for their markets, for their international prestige, for the welfare of their populations – were immense.

With Beijing, Trump may wave his power, but those steps come with ramifications. They come with a cost.

• The US president hails 'impressive' encounter with Xi but no agreement agreed
• Xi and Trump establish temporary truce as Beijing adopts strategic patience

For the opening segment, Trump's recent entry into world politics was successful.

Each visit was characterized by a blend of traditional commercial discussions – arrangements made under the shadow of the president's "reciprocal" duties – and personal accommodations that at times bordered on the subservient.

In Malaysia, Trump secured access to essential resources and made progress toward finalizing economic agreements with south-east Asian nations. He also presided over a agreement that should alleviate border tensions between Thailand and Cambodia – the type of "peace deal" the US leader enjoys to tout.

In Japan, Trump's helicopter soared near a famous structure displayed red, white and blue – with a summit in golden.

Newly elected Leader Takaichi described $550 billion in Japanese investments in the US and presented the president a present of a quarter-thousand cherry trees for America's semiquincentennial, and a golf equipment and case that belonged to the late leader, the murdered ex-leader who developed ties with Trump in his previous administration.

She also became the latest overseas counterpart to suggest Trump for his much-desired peace award.

Matching the effort, Korea received Trump with artillery performing a honor salute and a service ensemble that played the leader's song and YMCA – the band anthem that has turned into a political gathering standard.

President Lee Jae Myung held an "honour ceremony" for Trump during which he presented the president his country's highest medal and a model of an traditional ruler's coronet.

Midday meal with the Korean leader featured a "Conciliatory Treat" of gold-encrusted chocolate squares. Subsequently, the hosts provided the president vineyard wine at an intimate dinner in Trump's honor with multiple global figures present at the regional summit summit.

In the United States, Trump may be the target of "Anti-Monarchy" demonstrations by US citizens who disapprove of his authority-expanding increases of presidential power, but during his Asian swing he was received as monarchy.

And like the rulers of ancient times, the president came to South Korea demanding tribute – in the form of $two hundred billion in financial transfers, $20bn a year, from Korea to the US, to be invested at the direction of Trump's leadership. Approval on the details of those contributions contributed to that the duty level on Korean products to the United States would fall from 25% to fifteen percent.

The main event of the president's regional visit came in its last moments, nevertheless, as he sat down with Xi.

In that setting, the power dynamic between heads of the world's two largest economies was decidedly divergent than the interactions the president had with his overseas colleagues in prior visits.

Not present were all the ceremony and the spectacle. Without any service ensembles, no protocol units, no thoughtfully prepared dining selections celebrating bilateral friendship. Instead, the both heads and their senior advisors sat across a long white meeting furniture in a unremarkable military building just near the airstrip of Busan's global terminal.

It was possibly a demonstration of the high stakes that when Trump shook hands with Xi in Busan, he looked