Call it the melee of the middle-aged men.

We already know the main event. That would be Elon Musk versus Mark Zuckerberg in Las Vegas, or maybe the Colosseum in Rome. The rival tech billionaires are inching toward a cage match, brokered by Dana White, president of the Ultimate Fighting Championship.

And for an undercard, how about a sitting U.S. senator versus a union boss? Markwayne Mullin, an Oklahoma Republican, last week challenged Sean O’Brien, the general president of the International Brotherhood of Teamsters, to a mixed martial arts fight after Mr. O’Brien called him a “clown” and a “fraud” on Twitter.

In case that’s not enough testosterone, perhaps some feats of strength are in order. Robert Kennedy Jr. might be interested. The Democratic presidential candidate recently took his shirt off in Venice Beach to perform push-ups and incline bench presses — revealing an uncommonly defined upper body for anyone, let alone a 69-year-old. (He has a full decade on Jeff Bezos, who is also musclebound.) So too might Jamaal Bowman. On Thursday, the Democratic representative of New York posted to Twitter a video of himself bench-pressing 405 pounds.

For some powerful men, this is a season for peacocking. No longer content to embody the masculine ideals of financial, professional and political achievement — or simply to optimize their fitness, as tech chief executives have long done — suddenly these honchos want us to see the achievements of their bodies. Grappling, squeezing, flexing, dominating (or being dominated): These are no longer tired metaphors for corporate or intellectual conquest. They are literal descriptions of America’s big shots showing off as buff boys.

So, what’s with all these conspicuous displays of machismo? To start, they’re mostly just that — displays.

“A lot of it is spectacle,” said Andrew Reiner, a lecturer in men’s studies at Towson University and the author of the book “Better Boys, Better Men: The New Masculinity That Creates Greater Courage and Emotional Resiliency.” As Mr. Kennedy’s viral lifting session proved, a bit of well-timed machismo is prime fodder for the social media machine.

But, according to Mr. Reiner, these look-at-me behaviors also draw on something deeper: tropes of masculine honor and personal strength that American pop culture has been broadly moving away from, but may be rediscovering.

“It’s textbook, old-school, throwback masculinity,” Mr. Reiner said, pointing to Will Smith’s slap of Chris Rock at the 2022 Oscars — after Mr. Rock made a joke about Mr. Smith’s wife, the actress Jada Pinkett Smith — as a watershed moment.

One factor in the cage match moment is the increasing influence of mixed martial arts culture. Joe Rogan, a prominent fan of fights who holds a black belt in Brazilian jujitsu, reaches millions of people with his podcast, “The Joe Rogan Experience,” on which Mr. Musk, Mr. Kennedy and Mr. Zuckerberg have all appeared as guests. Mr. Mullin, the senator, had a short career as an M.M.A. fighter.

The Musk-Zuckerberg and Mullin-O’Brien back-and-forths recall the performative jawing of a boxing match weigh-in, and the athletic theater, or “kayfabe,” of professional wrestling, where wrestlers play characters who never acknowledge there is a script.

This blend of reality and fantasy became a key feature of American public life during the Trump years, according to Abraham Josephine Riesman, the author of “Ringmaster: Vince McMahon and the Unmaking of America.” The blurring of reality is key to understanding a world in which campy performances of heterosexual masculinity can seize our collective attention, Mx. Riesman said.

“There’s something about committing to a totally outsized parody that just works for the human brain,” she said.

Another common thread may be a measure of overcompensation. After being photographed shirtless last summer aboard a yacht (and subsequently ridiculed for his physique), Mr. Musk tweeted in October that he had been fasting and taking Wegovy, a prescription drug used to treat obesity. And although Mr. Zuckerberg, who is 5 feet 7 inches tall, is in fact a committed athlete, he has for years worn the title of nerd king, which he inherited from Bill Gates. (Recently, Mr. Zuckerberg has turned to training and competing in martial arts, and posting mirror selfies of his progress on Instagram.)

Meanwhile, for Mr. Kennedy, the shirtless romp draws a contrast with the Democratic front-runner, President Biden, who is 80 years old. “Getting in shape for my debates with President Biden!” Mr. Kennedy tweeted, alongside a video of himself doing push-ups.

The modern history of male politicians strutting and brawling dates back at least to Teddy Roosevelt in the early 1900s. Vladimir V. Putin, the Russian president and himself a judo black belt, was photographed shirtless on horseback in 2009. And Paul Ryan, the former speaker of the House and onetime vice-presidential candidate, posed with 40-pound dumbbells for Time magazine ahead of the 2012 presidential election.

More recently, the muscular former Democratic congressman John Delaney spoke to the news media in 2019 about his fitness routine while running for president. (Mr. Mullin’s bipartisan, CrossFit-inspired fitness routine was covered in The Times nearly a decade ago.)

Gary Meltz, a consultant who advises politicians and corporations on their image, said he thought Mr. Kennedy’s attempt to seem younger and stronger than Mr. Biden misread the electorate.

“It’s more akin to Putin sitting on top of a horse than something that will appeal to Democratic voters,” Mr. Meltz said.

Of course, women in leadership positions face scrutiny over their appearance and affect in ways Mr. Musk and Mr. Kennedy never would. Imagine, for example, how a female C.E.O. who displayed Mr. Musk’s apparent impulsiveness, aggression and vanity would be talked about.

“The margin with which women can display any kind of jealousy, resentment, ego, or desire to get ahead in any unfettered way is very narrow,” said Samhita Mukhopadhyay, the co-editor of the anthology “Nasty Women: Feminism, Resistance, and Revolution in Trump’s America” and the author of the forthcoming book “The Myth of Making It.”

Then again, the times may be changing. Marjorie Taylor Greene, the Georgia congresswoman and CrossFit aficionado who once shared a video of herself performing pull-ups and overhead presses, called her Republican colleague Lauren Boebert of Colorado a “little bitch” on the House floor last month. It was just the kind of barb one might expect before a cage match.