“Trade wars are good, and easy to win,” Donald Trump declared this spring. He may soon find out whether he was right. On Thursday his administration launched a multi-front assault on allies and renewed its threatened offensive against China. What constitutes “winning” is hard to say when the aims are so muddled and diffuse. But it may prove good for him, playing well to his base. The imposition of tariffs on steel and aluminium imports upholds a campaign promise, as well as his inaugural pledge that “it’s going to be only America first”.

All US presidents think first of the interests of Americans; they would not gain or retain the office otherwise. Yet rarely have these been construed so crudely. Most have realised that the country gains from international cooperation and a rules-based order which it did most to shape. Not so Mr Trump. But since he seems to regard his position as a performance instead of a job, outcomes are almost irrelevant.

That his message has resonated so strongly reflects the profound failure of the existing economic system to deliver for ordinary Americans. Globalisation made some rich and many enjoyed cheap consumer goods. Others saw their jobs and communities disappear. Free trade comes at a cost – as the Chinese clearly agree, given some of their own practices. Yet Mr Trump’s medicine will not cure the patient, and may well cause further damage. He is a snake oil salesman, not a physician.

The tariffs on Mexico and Canada are probably in part regarded as leverage in Nafta talks, although they seem more likely to derail a deal than achieve one. Like those on the EU, they may also be a warning to China: if we play this tough with our allies, expect us to be much more brutal with you. Commerce secretary Wilbur Ross arrives in Beijing on Saturday to press his counterparts to narrow the $375bn trade deficit. Beneath the economic row lies a broad and mounting antagonism across the US political class to China’s growing might and its challenge to US hegemony – fuelled by Beijing’s increasing authoritarianism at home and forcefulness in international relations. Yet it is hard to be certain what Mr Trump wants when bilateral relations have seen such abrupt reversals. A fortnight ago, the treasury secretary Steven Mnuchin said the trade war was “on hold”. This week, trade adviser Peter Navarro called that an “unfortunate soundbite”.

These divisions within the administration (though hardliners are in the ascendant) and concerns about the effects of tariffs on domestic manufacturers and possible retaliation explain some of the shifts. But Mr Trump’s impatience also prompts rash actions, sometimes unwound later. The glory of cutting a deal with North Korea has at times seemed the priority. A watchdog group notes that Ivanka Trump won approval for Chinese trademarks days before her father reversed a decision to ban Chinese telecoms firm ZTE – which broke US sanctions on Iran and North Korea – from buying US components.

Mr Trump believes that his business persona is the key to international success as well as domestic support: go in hard, see where you end up. But beating down a small supplier is one thing. Negotiating a complex world of overlapping rivalries and shared interests, from security to economics, is another. If protecting the US economy and encouraging China to play fair are his true priority, he needs a strategy and all the help he can get. Plenty in the EU and Asia share US concerns about unfair competition from China and its actions in the international realm. Alienating allies, as he has done repeatedly, can only be counterproductive. And if the US turns its back on the international system, why should anyone else abide by the rules?

Canada and Mexico have already announced counter-tariffs. A more cautious EU has opened a case at the World Trade Organization, but warns that American goods could yet face the pinch. China has threatened to target products including soybeans: it takes almost a third of the US harvest, mostly from Trump-supporting states. The risks of a full-scale global trade war between the world’s three largest economies are real. Any win that Mr Trump proclaims is likely to prove illusory for his voters.