The flattery was as obvious as it was effective. Seated at a dinner table in the Blue Room of the White House on Monday, Prime Minister Benjamin Netanyahu of Israel handed President Trump a piece of paper.

“I want to present to you, Mr. President, the letter I sent to the Nobel Prize committee,” Mr. Netanyahu said, with the news cameras rolling to capture the moment. “It’s nominating you for the Peace Prize. It’s well deserved, and you should get it.”

Mr. Trump declared the gesture from the prime minister “very meaningful,” though he has long said he believes the Nobel committee would never give him the prize.

The effort to curry favor was the latest evidence that many of the world’s leaders have figured Mr. Trump out. Heaping praise on the American president is the best way to manage him — even if it’s not entirely clear that the schmoozing leads to concrete benefits for their countries.

After once calling Mr. Trump a “bully,” Mark Carney, the prime minister of Canada, last month gushed over “your personal leadership of the United States.” Mark Rutte, the Secretary General of NATO, sent a private text to Mr. Trump hailing “your decisive action in Iran, that was truly extraordinary.” Mr. Trump made it public the next day.