The game theory of Trump's tariff threats

Why he’s picking on Canada and Mexico — and why he’s playing a dangerous game.

Having grown up in Michigan, a.k.a. the 11th province, I have a lot of Pan-American Pride. I love visiting Canada and Mexico. I think we United States Americans greatly underappreciate the benefits of having two relatively peaceful, democratic, and economically vibrant neighbors.

So I find President Trump’s bullying of Canada and Mexico with tariff policy unseemly. And I think bullying is the correct term. I’m happy to poke fun at Canada for, say, not having won a Stanley Cup since 1993. But it’s not great to see Toronto Raptors fans booing the Star Spangled Banner.¹ It’s all too on the nose, like the fake Boston Globe front page from 2017 that included the headline “Markets sink as trade war looms.”

Yesterday, Trump paused tariffs on Canada and Mexico, which he’d implemented by executive order over the weekend. Mexico was able to negotiate the delay by pledging to deploy 10,000 troops to the U.S. border to combat drug trafficking. Canada’s promises were vaguer. Justin Trudeau initially struck a more defiant tone and vowed retribution. But he’s the lamest of lame ducks, and Conservative leader Pierre Poilievre, Trudeau’s most likely replacement, had proposed to send Canadian troops to the US-Canada border.

A quick word about market reaction

Markets breathed a sigh of relief. The S&P 500, down 1.2 percent at the open on Monday, recovered about half of its losses over the day and most of the rest so far as I type this on Tuesday morning. As evidenced by Polymarket putting the odds of the tariffs being implemented as low as 24 percent over the weekend, trader types pretty clearly thought Trump was bluffing — even though Trump had previously announced that the tariffs would go into effect on Feb. 1. (Given how the Polymarket resolution terms were structured, the question resolved to “yes” even though the tariffs were quickly suspended.)

I was originally going to have more about the market reaction and what I see as a basically incorrect belief that markets can rein Trump in by having a tantrum in the form of a stock selloff. But let’s save most of that for a future newsletter. (Surely there will be another occasion in the future when Trump does something that Wall Street doesn’t like.) The short version is that I think this anthropomorphizes markets too much, treating them as having agency and being capable of strategic behavior when instead they’re made up of discrete participants who each have their own incentives. Markets can’t coordinate to “send Trump a message” — Wall Street can’t agree to massively sell off stocks today and then buy them back on Tuesday — because then you could be guaranteed a huge profit and undermine the plan just by defecting from the pact and buying the dip.

I can take some partial credit here for having put the chances of Canada and Mexico tariffs at 60 percent instead in my Trump predictions column, though that’s not exactly the most confident prediction and my terms were different than Polymarket’s.² My logic, though, sounds wise:

I suppose I can imagine these tariffs being implemented for a short period of time as a show of resolve before being rescinded.

To the extent I’m patting myself on the back, it’s because I think of Trump as capable of strategic behavior in a way that can be described reasonably well in game theory terms. He’s not a bumbling idiot; he sometimes plays his cards wrong, but he understands one basic concept well: leverage.

Canada and Mexico are highly dependent on US exports

The US has a lot of economic leverage over Canada and Mexico, leverage it has over no other countries in the world. And Trump can make a credible threat to employ that leverage. In fact, game theory suggests this is true even if tariffs would be mutually harmful, as they very probably would be, hurting the American consumer and inevitably triggering retaliation.

To be clear, this isn’t how I’d play my hand if I were president. There are too many ways it might go wrong. The concessions Trump might extract are minimal and require Canada and Mexico to capitulate in a way that might meet some narrow definition of rationality but ignore both human nature and domestic political pressure. He’s also ignoring the geopolitical consequences of alienating our friends. Canada, in particular, has been a loyal ally to the US. Even during Trump’s first administration, it voted the third-most often with the US in the United Nations, ahead of only Israel and Micronesia.³

Nevertheless, I’ve seen people scratching their heads about why Trump threatened higher tariffs on Canada and Mexico than on countries we have a more rivalrous relationship with — or on countries whose exports are less important to the American consumer. There were lot of good jokes on Twitter about how this was the geopolitical equivalent of the Luka Doncic trade.

But I don’t think the answer is so complicated. If you’re willing to make a particular set of assumptions and treat international trade as a sort of poker game — assumptions that I don’t think are broadly rational but might be a good approximation for the blinkered way in which Trump sees foreign relations — then there’s a cold, game-theoretical logic to his approach

In game theory terms, this isn’t mutually assured destruction or a game of chicken. A trade war would be very costly. But the costs aren’t infinite, and these countries have more to lose than we do.

Canada and Mexico have a lot going for them. They own resource-rich territory. They have diversified economies. And they have a prosperous next-door neighbor with whom they’ve mostly been on good terms for the past century-and-a-half.

The downside — not one that had seemed like a real risk until recently — is that their economies are incredibly dependent on American exports.

Here’s the data for the world’s 15 largest economies (with the EU countries rolled up into one). Not only does the United States receive 77 percent of Canada’s exports, but those exports represent 20 percent of the entire Canadian economy by GDP. For Mexico, the numbers are even more stark. We’re 79 percent of their exports and 26 percent of their GDP. Completely pausing trade with these countries might cause a recession in the United States, but it could trigger a depression in our neighbors.

By comparison, no country’s exports account for more than 2 percent of American GDP. Tariffs are still enough to cause plenty of pain for American consumers. But the situation is nonetheless asymmetric. Tariffs on Mexican exports would put 26 percent of their economy at risk versus 2 percent of ours.

We also run a trade deficit with most major economies; the exceptions are the UK, Brazil, and Australia. So while these countries could and probably would retaliate by placing tariffs on American imports, the relative impact is less. And the absolute impact is much less, just because our economy is so big and we produce a lot of stuff at home. The US economy is about 3 times larger than the rest of the Americas combined. We’re the bullies in this situation.

In theory, Trump has leverage…

But what does game theory say? Sorry if this is so on-brand — but there’s a direct analogy to poker, a case where solvers, a.k.a. fancy computer programs that explicitly calculate a Nash equilibrium, have derived the game-theory-approved answer.

In poker tournaments, big stacks have more leverage. If you have 10,000 chips and I have 100,000, then I represent a bigger threat to you than the other way around. I can put your entire tournament at risk by contesting a big pot, whereas you can at best extract a flesh wound.

This is despite the fact that you might nevertheless harm me. It’s not like I want to give away those 10,000 chips for nothing. In fact, an intrinsic mathematical property of the prize structure in poker tournaments is that any confrontation is harmful to all players contesting the pot and helpful to the other players who are just sitting around twiddling their thumbs checking their phones. (In tournaments, once you approach the prize money, you can literally make money just by doing nothing, hoping other players bust out so you can move up the prize ladder.) That doesn’t mean you should fold every hand⁴, but it’s a situation that calls for a more selective, tighter approach.

Again, however, the risks are asymmetric. If I represent an existential threat to you — I can cost you your tournament life or send your economy into a depression — and you represent a serious but nevertheless survivable threat to me, the game-theory equilibrium is that the big stacks become incredibly aggressive and bullying, in some cases raising literally every hand.

In the specific context of a poker tournament, a game where players are quite explicitly EV-maximizing and there’s also no real social price to pay for bullying — today, you’re the small stack, but in tomorrow’s tournament, the tables will be turned and you’ll be the big stack, so nobody takes this too personally — most players go along with the solvers. You raise seven-deuce offsuit as the big stack on the bubble of a poker tournament — the worst hand in poker. In extreme circumstances, your opponents may hem and haw and fold some a hand as strong as a pair of jacks, even if they know you’re raising every hand — or at least that’s what the math says to do.

…but trade wars are not a poker tournament

However, there are constraints on your leverage. Even under game theory optimal play, the smaller stacks are sometimes supposed to retaliate and raise, both because they often have a stronger hand given all the BS you’re playing and because it creates some deterrence. You’ll think twice about raising with such a weak hand in the future if they’ve shown a willingness to fight back.

And sometimes in poker — and very often in analogous situations in the real world — you’ll encounter a player who says fuck you and retaliates when you’re bullying them even if they’re making a −EV play and putting their own life at risk.

This behavior might be “irrational,” but I’m putting that term in scare quotes because the desire to seek revenge — to stand up against a bully even if it the odds are against you — may be a trait that’s selected for on an evolutionary basis because it contributes to the survival of your tribe, country or species. Yes, this quickly gets into extremely fraught territory, as everything involving evolutionary selection does. (There’s more about it in the book.) But if I know that people in your culture are willing to die for a cause, to defend their honor at all costs, that will make me less likely to fuck with you in the future.

To bring this back to the real world, this is what makes Trump’s strategy so risky. The game theory says that because the US economy has so much more leverage, he should be able to extract some minor concessions from Canada and Mexico by threatening a trade war. He doesn’t necessarily want a trade war⁵, but he’s betting his bluff won’t be called — and he’ll usually be right. And that’s basically what happened in Round 1. We threatened tariffs, and because Trump’s threats are fairly credible for reasons ranging from his ideological commitments to his reputation as a rogue actor, Canada and Mexico capitulated.

But this will likely build up a lot of resentment — nothing creates resentment like capitulating to bullies — and a lot more Leeroy Jenkins energy from our neighbors in the future. If Trump expects to extract some new form of tribute from Canada and Mexico every month in exchange for delaying tariffs, their leaders are eventually going to say fuck you — or their populace is going to elect new leaders. Wall Street might have been pleased by how the situation played out. But it should probably have sold off more when Trump pledged to implement the tariffs in the first place. This was a highly escalatory move with the potential to go badly next time we play the game.

1. In typical Canadian fashion, Raptors fans cheered the singer after she was done.

2. My prediction pertained to Trump implementing 25 percent tariffs on Canada or Mexico at any point before the 2028 elections — whereas for Polymarket, it was Canada and Mexico by the end of February.

3. The rest of the Americas haven’t voted with us nearly so often, for what it’s worth.

4. Although folding is +EV, you can sometimes make even more money by contesting the pot if your hand is strong enough.

5. I mean, maybe the real Trump doesn’t care, but Nash Equilibrium Trump is mostly hoping to use the threat of a trade war as leverage.