If you want to understand why the United Auto Workers union has evidently won its strikes against Detroit’s Big Three, it helps to return to the work of a 20th-century economist named Richard Lester.

Lester, a longtime Princeton professor, coined a phrase to describe wage negotiations between an employer and a worker: the “range of indeterminacy.” It captures the fact that wages are not a reflection simply of market forces, like a worker’s productivity or a company’s profits. In the real world, similar workers often earn different wages. Their wages fall somewhere in Lester’s range of indeterminacy.

Why? Most workers don’t know exactly how valuable their contributions are and therefore what their true market wage should be.

Company executives typically don’t know either, but the executives do have more information — about how much money different workers make and how productive each is. Employers also have more leverage. Companies employ many workers, and losing one of them is usually manageable. For most workers, by contrast, quitting over a pay dispute can create financial hardship.

For these reasons, workers’ pay often settles at the low end of the range of indeterminacy. In the relationship between an employer and an individual employee, the employer has more power. But there is an important adjective in that previous sentence: individual.

When employees band together, they can reduce the power imbalance. They can share information with one another and exert some leverage of their own on the bargaining process. A business that can afford to lose one worker over a pay dispute may not be able to lose dozens.

Of course, there is a term for a group of workers who come together to increase their bargaining power: a labor union.

Is Tesla next?

Over the past week, the Big Three — General Motors, Ford and Stellantis (which owns Chrysler) — have each agreed to wage increases that workers surely could not have received by asking nicely. The G.M. deal, announced yesterday, was the last of the three.

After adjusting for inflation, many workers seem set to receive roughly a 10 percent raise over the next four and a half years. By 2028, when the contract expires, many workers will make between $30 an hour and $42 an hour, or between $60,000 and $84,000 a year for full-time work.

The pay increases are the largest that autoworkers have received in decades, my colleagues Neal Boudette and Jack Ewing explain. The raises are also a reminder that organized labor has an unmatched record in reducing economic inequality.

A large academic study, using Gallup surveys covering millions of workers over decades, found that unionized workers typically made 10 percent to 20 percent more than similar non-unionized workers. The extra pay generally does not harm economic growth, the economists found. It instead often comes out of executive salaries and business profits, reducing inequality. Unions alter the division of the economic pie more than the pie’s size.

Or to put the idea in Lester’s terms, unions shift wages out of the low end of the range of indeterminacy.

To be clear, unions sometimes do win pay increases so large that wages exceed a reasonable range and hobble an employer. Unions can also block necessary changes in a company’s operations. Such overreach happened in parts of the auto industry during the 1970s, contributing to Detroit’s decline. Today, auto executives warn of a similar risk. The unions counter that the recent raises make up for years of wage stagnation — and that Detroit’s executives have received even larger raises recently.

I don’t pretend to know whether these wage increases will look reasonable in hindsight. It will depend partly on whether Chrysler, Ford and G.M. make more appealing vehicles in the years ahead than they did in the 1970s.

But it would be a mistake to assume that the executives are automatically correct that the wage increases are excessive. Wages make up less than 5 percent of the cost of many vehicles. And company executives in almost every industry often claim that wages are too high. They prefer it when wages are on the low end of the range of indeterminacy — partly because it leaves more money for the executives to take home.

A hat tip: I learned about Lester’s work from Lawrence Katz, a leading labor economist today. You can read The Times’s 1998 obituary of Lester.

More on the deals

• President Biden — who risked political capital by picketing with striking G.M. workers last month — called the deals “a testament to the power of unions.”

• The agreements include commitments by the companies to expand or reopen Midwestern factories that employ unionized workers.

• Shawn Fain, the president of the U.A.W., signaled that the union could soon begin drives to organize U.S. workers at Tesla, Toyota, Honda and BMW.

• Three young labor activists — who never worked in an auto factory — helped the union become more media savvy, The Wall Street Journal reports.

ISRAEL-HAMAS WAR

State of the War

• Israeli troops appear to be encircling Gaza City. These satellite images show how armored vehicles have approached the city’s outskirts.

• Benjamin Netanyahu said he would not consider a cease-fire: “Calls for a cease-fire are calls for Israel to surrender to Hamas.”

• Hamas released a video of three female hostages who described “unbearable conditions” and criticized Netanyahu. It was not clear whether the three were forced to record the video; Israeli officials called it “cruel psychological propaganda.”

• The United Nations described a desperate situation in Gaza and said the aid arriving was insufficient.

More Details

• Israel began its invasion in secrecy to surprise Hamas and buy itself time to determine its next move, Patrick Kingsley and Ronen Bergman write.

• The military said it had rescued its first hostage: Ori Megidish, a 19-year-old soldier. Hamas had captured her on Oct. 7.

• The U.N. agency that aids Gazans said 10 members of its staff had been killed in the past three days.

International Reaction

• The Biden administration, which at first fully supported Israel’s war on Hamas, has grown more critical. Officials said the humanitarian crisis in Gaza was a reason.

• In Las Vegas, a man was charged with threatening to kill Senator Jacky Rosen, a Nevada Democrat who is Jewish; he also suggested she was complicit in the deaths of Palestinians.

• A wave of antisemitism in Europe has some Jews worried about their safety, The Wall Street Journal reports.

MORE NEWS

Artificial intelligence

• Biden signed an executive order on A.I. It requires companies to share information with the government about systems that might threaten national security, among other things.

• The executive order is an attempt to harness the technology’s economic potential while minimizing its risks, Kevin Roose, a Times tech columnist, writes.

Politics

• A trial over whether Donald Trump should be disqualified from running for president because of his role on Jan. 6 began in Colorado.

• The Supreme Court seemed torn in a case about civil asset forfeiture — police officers’ seizure of property they suspect has been used in crime.

Business

• Twitter is now worth $19 billion, the company said. Elon Musk paid $44 billion for it a year ago.

• Sam Bankman-Fried faced harsh cross-examination from federal prosecutors, who grilled him about contradictions in the way he spoke about and ran his crypto company.

Other Big Stories

MORNING READS

TikTok famous: A trucker, a shepherd and a commercial fisherman have become celebrities on social media.

Bird brains: Scientists say they have evidence that roosters can recognize themselves in mirrors.

Lives Lived: Wanda Poltawska survived gruesome medical experiments in a Nazi concentration camp. She sought spiritual help from a Krakow priest who, decades later, became Pope John Paul II. She died at 101.

SPORTS

World Series: The Texas Rangers took a 2-1 lead over the Arizona Diamondbacks with a gutsy 3-1 road win.

N.F.L.: The Detroit Lions are 6-2, riding high after a 26-14 blowout win over the Las Vegas Raiders.

Sudden exit: Iowa informed the offensive coordinator Brian Ferentz, son of the team’s head coach, Kirk Ferentz, that he would not return next season. That ends an absurd saga for the Hawkeyes.

ARTS AND IDEAS

Now screaming: Looking for something spooky to watch tonight? Erik Piepenburg, a Times reporter and horror geek, lists 25 great scary movies you can stream, including:

• “Halloween” (1978), on Crackle. “When people ask me what my favorite horror movie is, John Carpenter’s groundbreaking shocker comes out on top,” Erik writes.

• “The Blair Witch Project” (1999), on Freevee. “The final minutes get my vote for the scariest horror movie ending.”

• “The Blob” (1958), on Max. “The era will look so foreign and the special effects so outdated that kids will find it to be just cartoony fun.”

More on culture

• Experts say it may be weeks or months before Los Angeles officials can determine how the actor Matthew Perry died. He was found in a hot tub.

• An exhibition at the Getty in Los Angeles reveals the Egyptian Book of the Dead — a compendium of spells for navigating the afterlife.

• The late night hosts said goodbye to Mike Pence’s presidential campaign.

THE MORNING RECOMMENDS …

GAMES