Matthew Giachelli got the call he anticipated on Thursday morning: The N.F.L. was moving the Rams’ playoff game to Arizona because of the wildfires raging in Los Angeles, and the league needed 200 gallons of paint pronto.

The game on Monday between the Rams and the Minnesota Vikings would now be held at State Farm Stadium outside Phoenix, and it had to look and feel as if it were being played in the Rams’ usual home, SoFi Stadium. That included painting the field with the team’s and league’s logos and colors. The hometown Cardinals, though, did not have some of the needed hues on hand, including the Rams’ blue and yellow.

Giachelli’s company, World Class Athletic Surfaces in tiny Leland, Miss., provides paint to most N.F.L. and top college teams. Within hours, he and his co-workers had loaded five-gallon buckets of nine custom paint colors, as well as stencils for the N.F.L. playoff logos, onto a truck that left Thursday afternoon on a 1,500-mile journey to Arizona.

“I definitely regret what’s going on in California, but I’m glad we could meet their needs,” said Giachelli, the vice president of production and distribution.

Getting the right paint was just one of hundreds of details that the league, the Rams, the Vikings, the host Arizona Cardinals and ASM Global, which operates State Farm Stadium, have juggled since the N.F.L. decided to move the wild-card round game.

The N.F.L. has canceled preseason games and postponed and moved regular-season games over the years because of hurricanes, snowstorms and other calamities. But it had not moved a winner-take-all playoff showdown since 1936, when the site of its championship game was changed from Boston to New York to drum up ticket sales.

A battalion of people — from the front-office workers to the training staffs to the thousands of game-day workers — have been mobilized on short notice. Each game, particularly in the playoffs, generates tens of millions of dollars for television networks, advertisers and stadium operators, and with the season coming down to its last few weeks, there was little margin for error.

“If it can be played, they play it, and in this case, it can be played in Glendale,” said Joe Buck, who will call the game for ESPN on Monday. “We’re in the playoffs now, and you’ve got all this pressure to get this first round finished before Kansas City and Detroit,” which had first-round byes, “get back in.”

A big reason the N.F.L. is the world’s most valuable league is scarcity. There are just 272 regular-season games and 13 playoff games, so each one is of critical importance to the 32 teams. (By contrast, there are about 400 Major League Baseball games every month during the season.) They are also critical to the owners of those teams and the league, as well as broadcast networks, sponsors and other companies that spend billions of dollars a year to attach their businesses and brands to the N.F.L.

It has not escaped notice that one of those businesses, State Farm, will have its name attached to Monday night’s broadcast less than a year after it announced that it would not renew 30,000 homeowner policies and 42,000 policies for commercial apartments in California. (The N.F.L. has donated $5 million to Los Angeles relief efforts.)

With so much riding on each contest, the N.F.L. does everything it can to play every game every year. When the league creates its season schedule each spring, it prepares contingency plans including an alternate site for each game. In 2022, when a massive snowstorm hit western New York, the Buffalo Bills played a home game at Ford Field in Detroit.

During the pandemic, outbreaks in locker rooms forced the league to postpone several games, though none were canceled. When pandemic conditions in Santa Clara County, Calif., deteriorated, the San Francisco 49ers moved to Arizona for a month, playing three home games in State Farm Stadium. Arizona was also a backstop in 2003 when the Chargers moved their home game against the Miami Dolphins because of fires in San Diego.

This time, the fires spread so quickly, the league decided to move the game five days before kickoff. Kevin Demoff, the president of the Rams, said the team had been in constant contact with officials in Los Angeles, who initially thought the game could be held at SoFi Stadium in Inglewood, which was unaffected by the fires.

But that changed midweek, when fires broke out close to the team’s training facility in Woodland Hills, forcing some players and staff to evacuate their homes and for one practice to be cut short. Demoff said he did not want the players and staff to be distracted, nor did he want city and county resources to be diverted for the game when they could be used to help others in need.

Moving the game is “just a recognition that there’s some things bigger than football and we owe this to our community to make sure that this game can be played safely and not be a distraction,” Demoff said Friday.

ESPN was on hold as well. Four of its production trucks were en route to Los Angeles from Pittsburgh when the league told the network on Wednesday night that the game could be moved to Glendale. The crews spent the night in Kingman, Ariz. On Thursday, the plan was to set up in both stadiums in case the league waited until Saturday to decide where to play. So the trucks continued on to Los Angeles while another set of trucks left for Glendale. When the N.F.L. said Thursday that the game had been moved, the first set of trucks, which had reached Ontario, Calif., turned around and arrived in Glendale with time to spare.

The Cardinals also helped out the Rams in ways beyond just lending their stadium. The team’s owner, Michael Bidwill, sent two team planes to Los Angeles to help the Rams get their entourage and equipment to Arizona.

The Biden administration issued sweeping rules on Monday governing how A.I. chips and models can be shared with foreign countries, in an attempt to set up a global framework that will guide how artificial intelligence spreads around the world in the years to come.

With the power of A.I. rapidly growing, the Biden administration said the rules were necessary to keep a transformational technology under the control of the United States and its allies, and out of the hands of adversaries that could use it to augment their militaries, carry out cyberattacks and otherwise threaten the United States.

Tech companies have protested the new rules, saying they threaten their sales and the future prospects of the American tech industry.

The rules put various limitations on the number of A.I. chips that companies can send to different countries, essentially dividing the world into three categories. The United States and 18 of its closest partners — including Britain, Canada, Germany, Japan, South Korea and Taiwan — are exempted from any restrictions and can buy A.I. chips freely.

Countries that are already subject to U.S. arms embargoes, like China and Russia, will continue to face a previously existing ban on A.I. chip purchases.

All other nations — most of the world — will be subject to caps restricting the number of A.I. chips that can be imported, though countries and companies are able to increase that number by entering into special agreements with the U.S. government. The rules could rankle some foreign governments: Even countries that are close trading partners or military allies of the United States, such as Mexico, Switzerland, Poland or Israel, will face restrictions on their ability to purchase larger amounts of American A.I. products.

The rules are aimed at stopping China from obtaining from other countries the technology it needs to produce artificial intelligence, after the United States banned such sales to China in recent years.

But the regulations also have broader goals: having allied countries be the location of choice for companies to build the world’s biggest data centers, in an effort to keep the most advanced A.I. models within the borders of the United States and its partners.

Governments around the world, particularly in the Middle East, have been pumping money into attracting and building enormous data centers, in a bid to become the next center for A.I. development.

Jake Sullivan, President Biden’s national security adviser, told reporters on Sunday that the rule would ensure that the infrastructure for training the most advanced artificial intelligence would be in the United States or in the jurisdiction of close allies, and “that capacity does not get offshored like chips and batteries and other industries that we’ve had to invest hundreds of billion dollars to bring back onshore.”

Mr. Sullivan said the rule would provide “greater clarity to our international partners and to industry,” while countering national security threats from malicious actors that could use “American technologies against us.”

It will be up to the Trump administration to decide whether to keep the new rules or how to enforce them. In a call with reporters on Sunday, Biden administration officials said that the rules had bipartisan support and that they had been in consultations with the incoming administration about them.

Though companies in China have begun to develop their own A.I. chips, the global market for such semiconductors is dominated by U.S. companies, particularly Nvidia. That dominance has given the U.S. government the ability to regulate the flow of A.I. technology worldwide, by restricting U.S. company exports.

Companies have protested those limitations, saying the restrictions could hamper innocuous or even beneficial types of computing, anger U.S. allies and ultimately push global buyers into buying non-American products, like those made by China.

In a statement, Ned Finkle, Nvidia’s vice president for government affairs, called the rule “unprecedented and misguided” and said it “threatens to derail innovation and economic growth worldwide.”

“Rather than mitigate any threat, the new Biden rules would only weaken America’s global competitiveness, undermining the innovation that has kept the U.S. ahead,” he said. Nvidia’s stock dipped nearly 3 percent in premarket trading on Monday.

Brad Smith, the president of Microsoft, said in a statement that the company was confident it could “comply fully with this rule’s high security standards and meet the technology needs of countries and customers around the world that rely on us.”

In a letter to Congressional leadership on Sunday that was viewed by The New York Times, Jason Oxman, the president of the Information Technology Industry Council, a group representing tech companies, asked Congress to step in and use its authority to overturn the action if the Trump administration did not.

John Neuffer, the president of the Semiconductor Industry Association, said his group was “deeply disappointed that a policy shift of this magnitude and impact is being rushed out the door days before a presidential transition and without any meaningful input from industry.”

“The stakes are high, and the timing is fraught,” Mr. Neuffer added.

The rules, which run more than 200 pages, also set up a system in which companies that operate data centers, like Microsoft and Google, can apply for special government accreditations.

In return for following certain security standards, these companies can then trade in A.I. chips more freely around the globe. The companies will still have to agree to keep 75 percent of their total A.I. computing power within the United States or allied countries, and to locate no more than 7 percent of their computing power in any single other nation.

The rules also set up the first controls on weights for A.I. models, the parameters unique to each model that determine how artificial intelligence makes its predictions. Companies setting up data centers abroad will be required to adopt security standards to protect this intellectual property and prevent adversaries from gaining access to them.

Governments facing restrictions can raise the number of A.I. chips they can import freely by signing agreements with the U.S. government, in which they would agree to align with U.S. goals for protecting A.I.

Under the guidance of the U.S. government, Microsoft struck an agreement to partner with an Emirati firm, G42, last year, in return for G42 eliminating Huawei equipment from its systems and taking other steps.

The Biden administration could issue more rules related to chips and A.I. in the coming days, including an executive order to encourage domestic energy generation for data centers, and new rules that aim to keep the most cutting-edge chips out of China, people familiar with the deliberations said.

The latter rule comes in response to an incident last year in which U.S. officials discovered that Huawei, the sanctioned Chinese telecom firm, had been obtaining components for its A.I. chips that were manufactured by a leading Taiwanese chip firm, in violation of U.S. export controls.

The announcements are among a flurry of new regulations that the Biden administration is rushing to issue ahead of the presidential turnover as it tries to close loopholes and cement its legacy on countering China’s technological development. The administration has issued new limits on exports of chip-making equipment to China and other countries, proposed new restrictions on Chinese drones, added new Chinese companies to a military blacklist, and hurried to finalize new subsidies for U.S. chip manufacturing.

But the A.I. regulations issued Monday appear to be among the most sweeping and consequential of these actions. Artificial intelligence is quickly transforming how scientists carry out research, how companies allocate tasks between their employees and how militaries operate. While A.I. has many beneficial uses, U.S. officials have grown more concerned that it could enable the development of new weapons, help countries surveil dissidents and otherwise upend the global balance of power.

Jimmy Goodrich, a senior adviser for technology analysis at the RAND Corporation, said the rules would create a framework for protecting U.S. security interests while still allowing firms to compete abroad. “They are also forward-looking, trying to preserve U.S. and allied-led supply chains before they are offshored to the highest subsidy bidder,” he said.