Stallone and Schwarzenegger: Anatomy of a Bromance
10/18/2013 AT 02:30 PM EDT
But the two action stars weren't always so chummy.
In 1982, Sylvester Stallone's Rocky III was in movie theaters – and so was his rival action hero Arnold Schwarzenegger's Conan the Barbarian. By 1984, a muscle-bound Schwarzenegger was the Terminator, while an equally brawny Stallone was basking in the box-office success of his Rambo franchise – and neither star wanted to concede the crown of world's manliest man.
"We really disliked each other intensely for 20 years," Stallone, 67, told PEOPLE of his costar, 66, on Tuesday at New York Special screening of Escape Plan, in which the duo devises a plan to break out of the most protected prison ever built.
Even so, Stallone admits, that wasn't always a bad thing. "Eventually you start to appreciate something … maybe the reason we were so competitive is what made us get where we are," he says. "Seriously, I think it helps. It's what gets you out of bed in the morning and go, 'Oh, I can't wait to get at it again.' "
Their Escape Plan director Mikael Hafström tells PEOPLE, "Now that they are a little bit older, I think they really enjoy the fact they have mutual experiences. They can have fun together, they can relax."
"They don't have to show anything to anyone anymore. You can tell they like being on set. They like telling old war stories, they like smoking their cigars. They earned it."
While friendly, their relationship is not always so civilized, with each pulling capers worthy of famous prankster George Clooney.
On the Escape Plan set, "There was so much testosterone, it was slippery," recalls Stallone. "We were constantly just trying to out-man each other. On the way out of a set, I'd call the police and have his car searched. And he had my car searched."
It wasn't just his car. Stallone once reported some activity around Schwarzenegger on a film set, saying, "'There's some suspicious stuff going on with that black van' … They literally strip-searched him! Then he got back at me."
Their favorite thing to do, says Stallone, is "probably the shopping on the weekends. He's an unbelievable shopper. He's a real badass but he likes to play chess. He's addicted to chess. Which I find... Are you joking? Water ski. Do something. Chess!"
Adds Stallone, "I don't know why we get along so well. It goes to show you: A good enemy is hard to find."