Athletes stroll through Olympic Park with them jangling in their pockets. Volunteers affix them to lanyards and swap them with journalists. A nattily dressed gentleman on my flight to Rio wore two dozen flamboyantly arrayed on his fedora.

They're Olympic pins, and here in Rio, they're the focus of a thriving barter economy. "It's the currency of the Games," says Dan Baker, the senior pin-head among a cadre of obsessive collectors displaying their wares at Olympic Park. "It's more important than money. In fact, you can get in some places with a pin where you probably couldn't get in if you handed them a $20 bill."

Pin trading dates to the dawn of the modern Olympics, when three designs were produced for the 1896 Games: One for judges, one for athletes, and one for officials. Production skyrocketed with the 1936 Games in Berlin; the Nazis manufactured them in the millions as tiny propaganda pieces.

In the years since, pins have become highly collectible. Nearly every country competing arrives with boxes of them, and some produce unique pins for individual sports—a new one this year celebrates the German cycling team. Many national press corps arrive with pins of their own design. The International Olympic Committee offers its own dignified designs, and of course sponsors hand pins of their own to anyone who asks.

Some of them are chintzy, like the pin I got from a PR rep for Bradesco, Brazil’s biggest bank. But most are surprisingly beautiful. They're small—lapel pins, not campaign buttons—with intricate detail and brilliant color. No one can say just how many exist, but I’ve seen hundreds in the three days since I arrived.

Obsessives like Baker are the most visible pin-swappers, but everyone does it. Volunteers exchange pins with journalists; journalists trade them amongst themselves; athletes swap with other athletes and hand them to taxi drivers as tips. Outside of Maracanã Stadium, a few hours before the Opening Ceremony, I saw an Egyptian athlete pull a fistful from the pockets of his orange sweatpants. Later, I saw a Moldovan man slump with disappointment after a US Organizing Committee official rebuffed his offer of a swap. Pin-seekers, too, know the thrill of victory and the agony of defeat.

Kyle VanHemert

Baker reckons he started the modern pin-head movement at Lake Placid during the 1980 Winter Games. Shortly before the Games opened, the Missouri native found himself playing poker with one of the official merchandise licensees. Baker took his winnings in souvenirs, including many pins.

While selling the merchandise, Baker discovered that many visitors carried pins. Some suggested trades. Baker started sticking them on his hat and vest because he had nowhere else to put them. Everyone coveted them. "People wanted 'em more than the ones I was selling," he says. He's been swapping since. Rio marks his 18th consecutive olympiad.

"It gets addictive," he says. "It's kind of like that Pokémon game. When you get a new one, you get excited, and that gets you motivated to find the next one." The comparison is apt: I’ve heard that the Games’ most coveted pin, created by a Japanese press group, features a tiny Pikachu.

As Baker explains supply and demand in the pin economy to me, a man clad entirely in Team USA gear thrusts a hand Baker's direction. “I don’t think you have this one,” he says.

"Beautiful pin," Baker says. It features the carbon fiber wheelchair BMW designed for US Paralympians. Turning it over in his hand, he discovers that the front wheel spins. "It moves!" he exclaims with delight. A nearby pin-head shouts to the fellow in USA gear, "You got another one of those?"

Kyle VanHemert

Pin-heads swap pins in a good-natured, take-whatever-you-like manner. They display them on foam boards easily stacked in a backpack at the end of the day. They display only those pins they're willing to part with; personal collections remain safely at home. Trading helps everyone stay in Olympic officials’ good graces—openly selling pins almost certainly would lead to expulsion from Olympic park. Barter inevitably gives way to sales though, especially as the Games draw to a close. In Sochi, a Russian in a sable coat and hat gave Baker $1,000 for a dozen good pins, a transaction Baker recounts with ambivalence.

He takes collecting seriously. Three days in and he’s already offered an Uber driver $500 Brazilian to drive him to each national team house. He figures 30 minutes at each would be plenty of time to do business.

His favorite pins evoke specific memories—conversations with folks from faraway places, or trades that transpired in unusual circumstances. Among his most memorable experiences is a trade he didn’t make during the 1980 Winter Olympiad. Someone offered him tickets to the US-Soviet hockey match. Baker declined, because he didn’t want to see the US lose. You know how that turned out. "That,” he says, “would have been a very good trade.”