President Trump is confident that the United States is winning its trade war with China. But on both sides of the Pacific, a bleaker recognition is taking hold: The world’s two largest economies are in the opening stages of a new economic Cold War, one that could persist well after Mr. Trump is out of office.

“This thing will last long,” Jack Ma, the billionaire chairman of Alibaba Group, warned a meeting of investors on Tuesday in Hangzhou, China. “If you want a short-term solution, there is no solution.”…

Yet it is not clear that either side will see a reason to back down. Aides to Mr. Trump say the president believes that the United States has the upper hand on China, with an ability to impose tariffs on a far larger number of goods than the Chinese can match given that America imports far more than it exports. And while the tariffs are unpopular with Republican lawmakers, farmers and manufacturers, his trade approach remains popular with his political base.

The Chinese side has its own political reasons to avoid capitulation. Acceding to Mr. Trump would be considered a sign of weakness for Mr. Xi, according to analysts.