For his latest doc, Oliver Stone and Vladimir Putin watched Dr Strangelove and had a natter about the horrors of nuclear war. Could May, Merkel and co learn a few things from the big screen?

Let’s call it Ruskie business: for his latest documentary, a four-hour series to be screened in the US next month, Oliver Stone has interviewed Vladimir Putin. It’s not the first time the Oscar-winning writer and director has had a face-to-face with a contentious world leader, having previously profiled Fidel Castro and Venezuela’s Hugo Chávez. But this project has an irresistible movie twist, featuring footage of Stone and Putin watching Dr Strangelove together. Apparently, the Russian president had never seen Stanley Kubrick’s pitch-black 1964 satire, so Stone screened it for him.

Hopefully, Putin learned something about the dangers of atomic brinksmanship from the film, rather than imagining himself shirtless, rodeo-riding a nuclear bomb. So, what other movies could educate our under-pressure leaders?

Theresa May: The Cook, the Thief, His Wife & Her Lover

The PM hasn’t had much luck with her dining choices recently. Her dinner with EU president Jean-Claude Juncker couldn’t have gone worse if the Deliveroo biker had gone to 10 Browning Street by mistake, while a recent softball photo op with a cone of chips gave her the unfortunate look of a shapeshifting alien infiltrator who skipped the briefing on how to chew like a human. A strong and stable movie might help: Peter Greenaway’s decadent, food-centred 1989 black comedy could provide both dinner-party pointers and purgative relief for May, from its tidy, bullet-point title to the fact that the wronged woman at its centre gets the better of her tormentors.

Angela Merkel: Rosemary’s Baby

Facebook Twitter Pinterest Keep calm and carry on, Angela ... Mia Farrow in Rosemary’s Baby. Photograph: Allstar

She may seem unflappable, but even Chancellor Merkel must be getting a little worried as some of Germany’s European peers veer dangerously to the right. But you don’t have to listen to your neighbours – even when they try to convince you that they simply have your best interests at heart. To that end, perhaps a screening of Roman Polanski’s 1968 psychological horror would help reaffirm Merkel’s belief that there are enormous benefits to keeping your head while all around are losing theirs to a satanic cult. It might also serve as a useful reminder that you shouldn’t blindly trust private healthcare practitioners, no matter who recommends them.

Nicola Sturgeon: They Live

Braveheart, shmaveheart. Former first minister of Scotland Alex Salmond once gleefully wrong-footed an expectant film festival audience by surprising them with a screening of John Carpenter’s Ghosts of Mars. Sturgeon, Salmond’s successor, would probably get more out of Carpenter’s 1988 prophetic satire They Live, a movie about fighting for autonomy that plays to the scrappy strengths of its unconventional lead. If Mel Gibson can become a symbol of Scottish independence, then “Rowdy” Roddy Piper – the Canadian wrestler who proudly rocked a kilt in the ring – can, too, and They Live still has interesting things to say about the sacrifices required to upend the established order, especially in the face of monolithic media messaging.

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Donald Trump: Idiocracy

The 45th president of the United States is no stranger to film sets, even if one-dimensional cameos in everything from Home Alone 2 to Zoolander don’t seem to have helped him understand how to talk in complete or even coherent sentences. We know the commander-in-chief loves single-minded action movies such as Jean-Claude Van Damme’s Bloodsport, even if his preference is to fast-forward through the boring bits. It seems obvious, then, but forcing Trump to watch Mike Judge’s garish 2006 future-comedy Idiocracy – a disaster movie where the disaster is dumbing-down – might make him realise belatedly that being as impulsive and hyperbolic as the energy-drink-slamming President Camacho of the year 2505 is no good thing.

Kim Jong-un: WarGames

Facebook Twitter Pinterest WarGames, with Matthew Broderick and Ally Sheedy. Photograph: RONALD GRANT

The obvious choice here is The Interview, the 2014 comedy flop about a vapid TV journalist (James Franco) landing a world-exclusive interview with, uh, North Korea’s supreme leader, Kim Jong-un (Randall Park). Judging by targeted cyber-attacks on Sony that turned the movie’s release into a stuttering fiasco, perhaps Kim had already decided the lesson he wanted to learn from it: get your retaliation in first. So, what about a Sunday matinee of WarGames, the beloved 1983 classic that features young Matthew Broderick accidentally hacking into a military supercomputer and triggering global thermonuclear war? It’s Dr Strangelove with training wheels, and its strong anti-war message apparently helped shape Ronald Reagan’s non-proliferation thinking. Surely Kim would empathise with another fresh-faced bad boy viewed suspiciously by international governments and move his finger away from the nuclear button?