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American leader visits overseas have traditionally been an chance to display the influence of the American nation on the world stage. Donald Trump's week-long swing through East Asia, by contrast, has been a show of the authority of the president – but also, at times, of that authority's boundaries.

Trump's destinations in Malaysia, Japan and Korea over the span of the initial days were an exercise in catering to a at times unpredictable American president. It was an admission that Trump, with the signature of a hand, could impose taxes and further steps that have the potential to harm the economies of trade-reliant countries.

His meeting with China's president Xi on Thursday, nevertheless, was something entirely different.

It was a meeting of equals on the international scene, where the risks for each country – for their financial health, for their international prestige, for the well-being of their citizens – were enormous.

With the Chinese, Trump may flick his authority, but those steps entail consequences. They carry a price.

• Trump describes 'remarkable' meeting with the Chinese leader but no pact agreed
• The Chinese president and Trump find short-term ceasefire as Beijing adopts strategic patience

For the first four days, Trump's most recent foray into global diplomacy was successful.

Each visit was punctuated by a blend of conventional trade negotiations – deals made under the shadow of Trump's "equivalent" tariffs – and special treatment that at times bordered on the obsequious.

In Malaysia, Trump gained entry to key materials and made advances toward completing trade arrangements with ASEAN countries. He also oversaw a pact that should ease frontier issues between Thailand and Cambodia – the sort of "peace deal" the American president loves to tout.

In Japan, the president's official aircraft passed by a Tokyo Tower lit red, white and blue – with a top in gilded.

Newly elected Head Sanai Takaichi outlined $half-trillion in Tokyo's funding in the US and offered the American president a gift of 250 flowering trees for the United States' semiquincentennial, and a golf equipment and carrier that belonged to Shinzo Abe, the murdered past head who bonded with Trump in his first term.

She also became the most recent international head to nominate the president for his highly-coveted international honor.

Matching the effort, the Korean government welcomed the president with guns discharging a traditional greeting and a military band that rendered the presidential anthem and YMCA – the Village People tune that has become a political gathering theme.

Head Lee held an "recognition ritual" for Trump during which he presented the US president his country's premier award and a replica of an historical royal headpiece.

Noon repast with Lee included a "Peacemaker's Dessert" of gilded baked goods. Later that day, the South Koreans offered Trump premium vintage at an intimate dinner in the president's honour with half-dozen world leaders attending the Asia-Pacific Economic Conference summit.

In the America, the president may be the focus of "No Kings" rallies by the public who oppose his boundary-testing increases of presidential power, but during his East Asia tour he was treated like monarchy.

And like the monarchs of history, the president arrived in Korea demanding tribute – in the shape of $200 billion in monetary contributions, $20bn a year, from South Korea to the US, to be used at the discretion of the president's leadership. Approval on the terms of those transfers helped ensure that the duty level on Korean exports to the United States would decrease from 25% to 15%.

The central moment of the president's regional visit took place in its final hours, however, as he encountered Xi.

In that setting, the power dynamic between counterparts of the global top two markets was noticeably distinct than the interactions the president had with his foreign counterparts in earlier stops.

Not present were typical pageantry and the spectacle. Lacking military bands, no protocol units, without meticulously designed menus celebrating mutual national affection. Rather, the both heads and their senior advisors sat across a long white meeting furniture in a plain armed forces facility just off the runway of the city of Busan's air transport hub.

It was possibly a reflection of the major consequences that when Trump shook hands with Xi in the Korean city, he seemed