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American leader visits overseas have typically been an chance to demonstrate the influence of the United States on the world stage. Trump's multi-day swing through Asian nations, conversely, has been a show of the authority of the president – but also, at moments, of that authority's constraints.

Trump's destinations in Malaysia, Japan and Korea over the course of the first four days were an demonstration in satisfying a at times volatile American president. It was an admission that Trump, with the stroke of a pen, could impose duties and additional actions that have the ability to harm the economies of export-dependent nations.

His sit-down with China's president Xi Jinping on Thursday, however, was a completely different scenario.

It was a session of counterparts on the world platform, where the stakes for each country – for their economies, for their international prestige, for the welfare of their people – were enormous.

With Beijing, Trump may use his pen, but these moves involve consequences. They come with a price.

• Trump hails 'remarkable' meeting with Xi but no agreement finalized
• Xi and Trump reach short-term ceasefire as China pursues extended strategy

For the initial phase, the president's recent foray into international relations was uneventful.

Each stop was punctuated by a mix of conventional trade negotiations – deals made under the shadow of the president's "equivalent" taxes – and special treatment that at moments approached the obsequious.

In the Malaysian stop, the president obtained entry to essential resources and made progress toward concluding commercial deals with regional partners. He also led a pact that should reduce frontier issues between Thailand and Cambodia – the sort of "truce" the American president loves to promote.

In the Japanese leg, Trump's Marine One soared near a landmark tower illuminated American colors – with a top in Trumpian gold.

Freshly appointed Head Takaichi described $550bn in Japanese investments in the United States and presented the US leader a gift of 250 flowering trees for the United States' 250th birthday, and a sports gear and bag that came from Shinzo Abe, the killed past head who developed ties with the president in his first term.

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

Matching the effort, Korea greeted the president with guns performing a traditional greeting and a military band that performed the presidential anthem and the Village People song – the Village People song that has evolved into a Trump rally anthem.

Head Lee held an "recognition ritual" for Trump during which he awarded the US president his nation's highest medal and a replica of an ancient Korean dynastic crown.

Noon repast with Lee included a "Conciliatory Treat" of gold-covered baked goods. Afterward, the South Koreans provided the president premium vintage at an intimate dinner in the president's honor with half-dozen world leaders attending the regional summit meeting.

In the America, the president may be the target of "Anti-Authority" rallies by US citizens who reject his boundary-testing expansions of presidential power, but during his Asian tour he was handled as monarchy.

And like the monarchs of old, the president arrived in South Korea requesting payment – in the guise of $200 billion in cash payments, $20 billion a year, from South Korea to the US, to be invested at the direction of Trump's administration. Agreement on the conditions of those transfers contributed to that the duty level on South Korean exports to the America would decrease from 25% to 15%.

The central moment of the president's Asia trip occurred in its final hours, though, as he sat down with Xi.

In that setting, the power dynamic between counterparts of the global top two markets was markedly distinct than the exchanges the president had with his international peers in prior visits.

Missing were typical ceremony and the display. Without any armed forces orchestras, without honour guards, no thoughtfully prepared menus honoring mutual national affection. Instead, the both heads and their top aides sat across a long white meeting furniture in a plain armed forces facility just off the runway of the southern port's global terminal.

It was likely a demonstration of the major consequences that when Trump made contact with the Chinese leader in the Korean city, he appeared