Much of the markets’ mixed reaction reflects uncertainty about a new president who has never held public office, leaving political leaders, business executives and international institutions to make bets on how a Trump administration may rewrite rules that have governed global affairs under American presidents of both parties.

“For allies and adversaries alike, the election of Donald Trump represents the likely abandonment of a decades-old U.S. commitment to uphold the global order,” said Ivo Daalder, a former United States ambassador to NATO who is now president of the Chicago Council on Global Affairs.

For some, there was initially a promising forecast. American and foreign stock markets climbed in what some analysts called “the Trump bump.” The Dow Jones industrial average has broken several records since the election, and last week topped 19,000 for the first time amid expectations of more business-friendly regulatory policies. Investment banks like Goldman Sachs have fared particularly well.

European firms have seen stock prices rise, too. Deutsche Bank, whose shares shot up as high as 17 percent after the election, has reasons for optimism beyond its longtime ties to Mr. Trump’s businesses. With the Justice Department proposing a $14 billion fine as it begins negotiations with the bank over its handling of mortgage-backed securities in the 2008 financial crisis, some in Germany hope a new administration will ease up and loosen regulations.

Another company that has seen its share value increase since the election is Magal Security Systems, an Israeli firm that helped develop high-tech security barriers around Gaza and the West Bank. With Mr. Trump’s promise to build a wall along the border with Mexico, investors expect that firms like Magal could get some of the business. Magal’s shares rose as high as 24 percent above their pre-election level, with trading volume as much as 150 times higher.

For the same reason, Mexico has taken an economic hit since the election. Besides the wall, Mr. Trump has vowed to withdraw from the North American Free Trade Agreement. Mexico’s peso has fallen sharply, and its central bank last week slashed its growth projection for next year, citing “the electoral process in the United States.”

Other economies have reacted with trepidation amid fears that Mr. Trump’s policies may drive up interest rates and inflation, an expectation that some traders call Trumpflation.

Some countries are trying to figure out how to respond in other ways. Leaders of NATO allies are looking at increasing military spending in response to Mr. Trump’s insistence that they pay a greater share of their defense. Lithuania last week chose a new prime minister, who renewed the nation’s promise to raise security spending.

In the Philippines, where President Rodrigo Duterte has feuded with President Obama, the government has tried to gain favor in Mr. Trump’s Washington. Mr. Duterte named as his new trade envoy to the United States Jose E. B. Antonio, a real estate tycoon who is helping build Trump Tower Manila. After Britain rebuffed Mr. Trump’s suggestion to name Nigel Farage, a leader of the “Brexit” campaign to leave the European Union, as ambassador to the United States, The Times of London reported that Mr. Farage may move to America anyway.

In many places, there is still much head scratching over Mr. Trump. The mass-circulation Bild Zeitung in Germany secured exclusive rights to translating into German the whole interview Mr. Trump gave to The New York Times last week. Bungeishunju, the Japanese publisher of “Trump Revealed,” by the Washington Post journalists Michael Kranish and Marc Fisher, reprinted an additional 10,000 copies.

In China, initial optimism about Mr. Trump is giving way to skepticism. “We should stop imagining what benefits Trump’s election could bring to China,” Zhu Chenghu, a retired major general, said at a seminar at the China Academy of Social Sciences in Beijing on Friday. “He will return to the traditional policies that rely on the role of the U.S. dollar and seek expansion overseas.”

Mr. Trump’s election is getting credit, or blame, for all sorts of events, no matter how tangential. In Russia, a newspaper interviewed an analyst who suggested that the arrest of a cabinet minister on bribery charges may have resulted from Mr. Trump’s success because Moscow no longer had to fear going after protégés of reformers who were once close to Washington.

Nowhere has the Trump Effect been more visible than in Jerusalem, where the political right has openly rejoiced at the election. Prime Minister Benjamin Netanyahu, who has had a prickly relationship with Mr. Obama, has made clear to associates that he is overjoyed at Mr. Trump’s ascension.

Members of Mr. Netanyahu’s coalition expect Mr. Trump to abandon the practice of Mr. Obama and presidents of both parties who tried to restrain Israel from building housing in the West Bank and East Jerusalem. Shortly after the election, a Trump adviser said settlements were not an obstacle to peace, appearing to have adopted the argument Mr. Netanyahu makes.

“The next few weeks present a unique window of opportunity for Israel,” Naftali Bennett, who leads a pro-settler party in Mr. Netanyahu’s cabinet, told a conference sponsored by The Jerusalem Post last week. After years of American pressure, he added, “it’s ours to decide.”

Betty Herschman, the director of international relations for Ir Amim, a group that opposes settlement construction, said it was too early to know what Mr. Trump’s policy would actually be. But she said one thing was clear: “The Israeli right is already celebrating.”

A case in point was last week’s decision on 500 new housing units in Ramat Shlomo, an ultra-Orthodox neighborhood of annexed East Jerusalem across the “green line” delineating the border that existed until Israel won the 1967 war. The development had been in the works for years without being built. An announcement that it would proceed in 2010 while Vice President Joseph R. Biden Jr. was visiting Israel infuriated Mr. Obama and his team.

Brachie Sprung, a spokeswoman for Mayor Nir Barkat, said last week’s action by the municipal planning committee was a result of the developer’s coming back to the city with revisions to his plan that required new approval.

“There has been no political statement here with this piece of land,” she said.

But it was easy to see the move in the context of the emerging Trump era. Meir Turgeman, the deputy mayor who leads the planning committee, had just days earlier promised to advance 7,000 housing units that were delayed under American pressure, and he named Ramat Shlomo as an example.

“I intend to exploit the change of the guard in the U.S.A. and bring them to approval,” Mr. Turgeman told Israel’s Channel 2. Until now, he said, there had been pressure from Mr. Netanyahu’s office not to proceed to avoid angering Washington. “That’s over. From now, we intend to take the plans out of deep freeze.”