But looming over the private dinner is a question: Did Mr. Trump and Mr. Zuckerberg reach some kind of accommodation? Mr. Zuckerberg needs, and appears to be getting, a pass both on angry tweets from the president and the serious threats of lawsuits and regulation that face other big tech companies. Mr. Trump needs access to Facebook’s advertising platform and its viral power.

Both men are getting what they want, and it’s fair to wonder whether this is a mere alignment of interests or something more.

“I believe they have a deal,” said Roger McNamee, an early Facebook investor who is now a fierce critic, who added that it was “probably implied rather than explicit.”

“Mark’s deal with Trump is highly utilitarian,” he said. “It’s basically about getting free rein and protection from regulation. Trump needs Facebook’s thumb on the scale to win this election.”