“The word ‘headquarters’ is a nontechnical, nonlegal term, but it plays well in the press to talk like this,” Mr. O’Kelley said. “It was a great P.R. move in all kinds of ways.”

Qinghai Wang, a finance professor at the University of Central Florida who has studied corporate headquarters, agreed.

“Corporate headquarters, or at least the part that is central to decision-making, should be just in one place,” he said. “Boeing, another Seattle company that moved headquarters more than 10 years ago, only moved a few hundred people to Chicago. Amazon is a big company, and it has a very big headquarters already.”

At least one expert realized some time ago how the game would end.

“Don’t be surprised if later this year, Amazon announces that it’s going to have more than one HQ2,” the City Observatory, a think tank in Portland, Ore., said in an essay posted in January. One reason: “If a single winner is announced, and its competitors are dismissed, then Amazon’s negotiating position becomes much weaker,” the essay said. Having multiple winners, on the other hand, would allow the company to play one off the other.

Even as the news sank in on Monday, some people rued the lost chance that Amazon would do something truly transformative — not just for the company, but for its new home.

“Big tech is at a pivotal moment, and Amazon is at the head of the class,” said Scott Phillips, an entrepreneur who submitted a proposal to build an enormous city for Amazon in rural Oklahoma. “It is time for them to aggressively think not just about their bottom line but about ways they can do right by the world.”