If President-elect Donald J. Trump meant what he said, then the world may one day look back to recall that the first superpower nuclear arms race since the Cold War was announced by two pajama-clad talk show hosts.

“Let it be an arms race. We will outmatch them at every pass and outlast them all,” Mika Brzezinski, of MSNBC’s “Morning Joe” program, said on Friday. She and her co-host, curled up in holiday-themed nightwear in front of a fake fireplace, said the quote was a statement from Mr. Trump, elaborating on a Twitter message on nuclear weapons.

Mr. Trump has a history of bluster and his declarations may turn out to be bluffs. But should he follow through on instigating a nuclear arms race, the consequences could be severe. Best estimates of likely Russian and Chinese responses offer a concerning guide. So do lessons from the Cold War arms race, which brought the world so close to the brink that once-hostile American and Soviet adversaries worked to reverse the competition they had once seen as essential.

What is the aim of an arms race?

Nuclear arms races are not usually something that states set out to provoke, but are pulled into against their wills.