The U.S.-China trade war, according to game theory

This is Planet Money from NPR. Over the last few months, US-China trade relations have been... Kind of bizarre. Like, it is unclear what these two countries are even trying to accomplish. There was President Donald Trump's big tariff announcement on April 2nd, then China retaliated, then... Trump retaliated for that retaliation. For a while, the U.S. put tariffs of at least 145% on Chinese goods coming into the U.S.

China then put 125% tariffs on US goods. The rhetoric from both sides got pretty heated. Here's President Trump. Our country and its taxpayers have been ripped off for more than 50 years. But it is not going to happen anymore. It's not going to happen. And in China, the Ministry of Foreign Affairs put out this almost like political campaign video. The narrator is saying the U.S. has stirred up a global tariff storm. You see lightning and a protest march.

And then he's like, history has proven compromise won't earn you mercy. Kneeling only invites more bullying. No one was going to back down. Earlier this month, everyone backed down. And it was announced that tariffs were lowered to 30% on Chinese goods and 10% on American goods. And then this week, two separate courts ruled that actually maybe a lot of the new U.S. tariffs are illegal, but the White House has appealed. It's very, it's disorienting, but it's also fascinating.

We called up trade economist Emily Blanchard to help us figure out how we should even begin to try to make sense of all of this, or at least the trade war part of all of this. It is not the easiest moment, we should say, to get time with Emily. I just did a panel at 12. I'm doing another panel at 5. We have a national security and economics conference here all day tomorrow.

The reason everyone wants to talk to Emily right now is because she has lived all of this stuff. Currently, she teaches at Dartmouth's business school. But during the Biden administration, she was the chief economist at the State Department. And Emily told us the tool she keeps returning to to make sense of all of this chaos is this one particular branch of economics, game theory. Behavior, choices, is always the reflection of your own incentives, right?

It's like, what do you want to have happen? And game theory is really just saying, well, what happens is not only a function of your choices, it's also a function of the choices of others. Game theory can show you how strategies bend and shift when I think that you think that I'll do one thing and you think that I think that you'll do this other thing. And using game theory, economists like Emily can at least...

try to untangle what the U.S. and China are up to, how exactly they're fighting this trade war we suddenly find ourselves in the middle of. The first step in this analysis is to decide... which of the many games game theorists have modeled is even the right one for the particular situation. You've got the prisoner's dilemma, the stag hunt, the dictator game, even chicken, you know, where we drive right at each other until one of us swerves out of the way.

That can be modeled in game theory. Then, once the economists know what game is being played, they will be able to identify the optimal strategy for that game. But Emily says when she looks at this trade war between the U.S. and China, she isn't even sure the two sides have done the first step of identifying the game. What happens if you...

think you're playing one game but in fact you're playing a very different game. What are the consequences of that? It's very bad. If you're playing the optimal strategy to the game that you're not in, the odds that you... really have the optimal strategy are very, very low. Hello and welcome to Planet Money. I'm Keith Romer. And I'm Amanda Aronchik.

Today on the show, what game is the US playing in its trade war with China? We will take a look at four possible contenders to see what each of them can teach us about the American and Chinese strategies. and about how this whole trade war might end up playing out.

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When Emily Blanchard was the chief economist at the State Department, she had a front row seat to how America's trade strategy was worked out. Now she's on the outside looking in. keeping a close eye on everything folks in D.C. and Beijing are saying and doing, and then using that as clues to how this trade war might go down.

I'm trying to back out from observed behavior and figure out, like, what do they think the game is? And then what's their strategy? So we asked Emily to be kind of our trade and diplomacy interpreter. She says there are clues to what game theory game the U.S. is playing in the ways President Trump tends to talk about trade negotiations. We're going to sit down and we're going to put very fair numbers down and we're going to say...

Here's what this country, what we want. You know, China, you have to buy another billion dollars worth of American wheat next year. And they'll either say, great, and they'll start shopping, or they'll say, not good. We're not going to do it. I said, that's OK. You don't have to shop. So which game is Trump playing? To Emily, it looks like he was thinking in terms of one in particular. I think...

Many of the choices of the administration and the statements of the Trump administration and the president himself kind of suggest to me that he thinks maybe this is a take it or leave it game, right? More the U.S. It's big. It's powerful. We're going first. We're going to offer you a deal and you can take it or leave it. In game theory, a take it or leave it game is known as an ultimatum game.

And to illustrate how it works, Amanda, you and I are going to play a quick version of the game right now. You're going to give me an ultimatum and I'm going to have to decide whether I want it or don't want it? Basically, yes. But there are some rules. An ultimatum game is a really simple game. One player is called a proposer and the other player is a responder. And the proposer has all the power.

Okay, Amanda, in our game, I will be the proposer. You will be the responder. Make sense? Yes, I will respond to your offer. Right. So before we started recording, I had our executive producer, Alex Goldmark, Venmo me $100. Actual dollars.

Yeah, yeah, yeah. And so now as the proposer, I have to decide how much of that $100 I'm going to offer to you, how much I'm going to keep for myself. And this is where you, as the responder, have a little bit of power in this game. You're going to have one choice. You can either accept the offer I give you and we both get to keep our shares of the money or you can reject the offer and neither of us gets anything. And I have to Venmo the whole hundred bucks back to Alex.

Do you get the terms? I think I understand the terms. Okay. I'm going to open up Venmo. Look for Amanda Aranchik. I'm writing down my offer, and I'm just going to show you this screen of what I'm offering you, and you tell me whether you would like to accept this offer or reject it. Okay, so yeah, as expected, the offer is $1. So basically, Keith will get $99 and I will get $1. So do I want Keith to suffer?

and get nothing just because I feel like his offer was pitiful and small and sad? Or do I want a dollar? And you know what, dude? I'll take the dollar. I didn't have a dollar five seconds ago. Now I'm going to have a dollar. I'll take it. A very Planet Money response. Pay, Amanda Aranchik. What's this for? Game theory. Pay. Oh, I got it. Game theory. Thank you, Keith. Thanks, Alex. Thanks, Planet Money. Okay. So, Amanda, the strategy, we actually...

both just used, is what's known as the optimal strategy, right? You chose the best rational path. Emily told me that we arrived at what game theory calls an equilibrium. where neither of us could have improved our outcome by deviating from the strategy we chose. Given that the responder has no outside option.

Like they get zero if they reject or they get whatever has been offered to them. The equilibrium of the game is the proposer offers virtually nothing and the responder just takes it. That was me. Well, I'm the guy who just took it. I will say, Amanda, Emily did mention that when they bring volunteers into the lab to play this game, a lot of them behave the way that you were sort of pressuring me to behave.

Actually, if you play these games in an experimental setting, you actually don't see very often that perfect equilibrium. Instead, you see splits that are... A lot closer to 50-50 than you would expect. So other kinder people are more likely to give $50? Is that what she's saying? Sure, sure, sure, sure, sure. But Emily says forget about kindness.

And for that matter, forget about what the right way to play the ultimatum game is. She says the part worth paying attention to in all of this is the White House's hunch that they are playing an ultimatum game at all. Crucially, it's assigned itself. the role of proposer, right? We have all the power, you have none. I actually don't think that's really the game that we should be playing or that we are playing because there's more to it than that.

Yeah, if it really was an ultimatum game, the US could have just said to China, Here are all the things we want. You have to crack down on fentanyl and intellectual property theft and buy more soybeans. And in exchange, we will keep our tariffs low. And China would have had to take that deal or leave it. But...

That is not what they did in real life, right? China fought back. They jacked up their own tariffs. And because China had the ability to fight back, unlike me in your sneaky game, they could do more than just take it. Or leave it. The trade war was never really an ultimatum game at all. Exactly. So let's consider some other possibilities.

So far, we've been thinking about this mostly from the U.S. perspective. But the whole point of game theory is that there are two sides to this interaction. And now we're going to look at things from the Chinese side of things. For that, we reached out to China expert Yun Soon. The most commonly used framing from media, from experts, is a game of chicken. Yun is the director of the China program at security think tank, the Stimson Center.

In A Game of Chicken, the model is two people in cars driving as fast as they can at each other and daring the other one to get out of the way. That's the metaphor? That is a metaphor. And that's what we... basically saw for the first half of April when U.S. escalated the tariff and the Chinese countered, and then U.S. escalated the tariff again, and the Chinese countered again. So neither side was willing to concede.

Keith, are you going to make me play Game of Chicken against you? Because I'll win. I checked with HR. We're actually not allowed to. So we are going to skip that one. Youn says, thinking of the U.S.-China trade war as a game of chicken. makes the most sense when you are focused on the two leaders involved. It's really important politically for both Donald Trump and Xi Jinping to be perceived in their own countries as these strong men who are never going to back down.

And the first one to blink or to appear soft is going to lose a lot of the leadership credibility that they prioritize. But, Yoon says Trump and Xi playing chicken with each other does not capture everything that is going on here. In part, that's because chicken is what's called a one-shot game. You play it once. Someone veers off to the side, or the two cars crash into each other, and then the game is over.

But looking at the long run, I think this is not just a game of chicken, because game of chicken by default is a temporary or a short ephemeral stage.

I think a more accurate description is, in fact, a war of attrition. And in a war of attrition? Importantly, there are a lot of turns. Time passes. The risk isn't so much one big smash up as it is slowly bleeding away all of your resources. The strategy here comes down to two big factors. The first is how valuable it is to you to come out ahead. Seems clear that both the US and China...

really want to win this trade war. Right. So then you look at the second factor, which is how much it costs each side to keep playing the War of Attrition game, how much damage they can take and for how long. And Yun says this is where the analysis of which country can better survive this trade war gets really interesting. Going into the trade war, there was a conviction on the U.S. side that because the Chinese economy is weak.

And Chinese economy has been very reliant on export to generate growth that were going to prevail. The Chinese are going to fold because they cannot afford a sustained trade. war or sustained high tariff, which will essentially kill their export to the United States. Because, yes, growth had slowed in China. The housing market had crashed. Unemployment was up. But, Yun says, in a lot of ways, China was actually super well prepared for a trade war of attrition.

This is not the first time they have to deal with a trade war with Trump administration, right? The last round of trade war, in fact, started in 2018. And some of those tariffs have still remained in effect as of today. And the Chinese have been preparing for this war of attrition kind of ever since. The Chinese government very intentionally rebuilt supply chains for goods that Chinese consumers rely on so that the country would be less vulnerable to trade restrictions.

And Chinese companies have gotten way more savvy at getting around U.S. tariffs by moving some of their production to intermediate countries like Vietnam or Mexico, where tariffs are lower, and then shipping to the U.S. from there. Or, Byun says, look at the different roles China and the U.S. play in each other's economies. On the U.S. side, giant trade barriers create a supply shock. Where's all our stuff going to come from?

On the Chinese side, they create a demand shock. Who's going to buy all the stuff we make? And those shocks play out on different timelines. I think the shock for the Chinese economy is much longer term because they will realize... gradually that, oh, wait a minute, our export industry is gone, or all these factories that's used to export to the U.S. market, that is gone. But those impacts are not immediately...

So, in fact, when I was in China in April, people were living their lives as normal. Finally, Yun says, if you want to understand which country was in a better place to win a war of attrition... Look at the difference in how the U.S. and China are set up politically. I think China is always going to have an advantage because it is an authoritarian state.

The Chinese government keeps pretty tight control over the media, so less overt criticism of their policies there and less super visible pushback from the Chinese people. I think the Chinese public opinion is going to exert so much less pressure on Beijing in terms of changing the course of this head-on collision, if you will. In the US, on the other hand… After the introduction of the tariffs, stock market became extremely volatile. Economists were predicting a recession.

And last but not least, we're also seeing the retail industries start to panic and customers start to panic. In retrospect, it does seem like it was costing the U.S. government a lot more politically to keep playing the war of attrition than it was costing the Chinese government. Which might have been part of the motivation for Treasury Secretary Scott Besant hopping on a plane to Switzerland to negotiate that 90-day pause on the new tariffs. I think it's a major...

The watershed significance of this round is that the Chinese come to see that Trump is vulnerable. After the Liberation Day, how Trump has reacted to the volatility on the stock market, on the bond market, and to the U.S. consumers, I think that suddenly made the Chinese realize that, oh, he's... He's not invincible. He's actually susceptible to domestic pressure.

And I suspect that in the future, if there is going to be escalation or negotiation again, that the Chinese will exploit those vulnerabilities. Yun sees this 90-day pause as something like a temporary ceasefire. She doesn't think either side wants to pull out the 100-plus percent tariffs again, but she also thinks there will be lots more little escalations in different sectors of the economy while the two countries try to find a way to win the game.

After the break, we consider one last possibility for the game the U.S. and China might be playing. A game where maybe we can all walk away happy. Potentially. If everyone can just figure out how to play it right.

Up to this point, all the games we've been talking about, the ultimatum game, chicken, the war of attrition, they are games where one player wins and the other player loses. They often play out as zero-sum games. But trade economists like Emily Blanchard like to model trade using a different game, a game that shows how two countries cooperating on trade can actually be good for both sides.

The aggregate pie and both you and me individually, we will both be better off if we cooperate. So that's viewing trade and economic interaction as positive sum. The game economists turn to over and over again to model this is called The Prisoner's Dilemma. In The Prisoner's Dilemma, you have this potential for win-win games. Okay, the prisoner's dilemma works like this. Two people, let's say their names are...

Keith and Amanda are arrested for a bank robbery that we did, in fact, commit last weekend. Good job, us. The cops have caught us, though, and they pull us into separate rooms, right? And they interrogate us individually on our own. You know what? I'm going to throw you under the bus because of that whole dollar thing. I would not have told me that ahead of time, but all right. Each of us in this game has a choice, right? We are the prisoners who are facing a dilemma. Either we can...

blab to the police about what we know about what happened, or we can stay totally silent and we don't say a word. Amanda, as you might imagine, you and I are going to go ahead and play this game right now. I'm going to give you the terms. You ready? Yeah, I'm ready. So again, this is going to be about money. Okay. If we both stay silent and don't tell the police anything, we get the like lower sentence. And that means we each have to Venmo Alex Goldmark $10.

Or if one of us rats the other one out and the other one stays silent, the ratter-outer goes scot-free, pays nothing to Alex Goldmark, and the one who stays silent has to pay... $100 to Alex Goldmark. And then in the last case, if we both rat each other out, we both have to Venmo Alex $30. Got it? Okay. So I want you on a piece of paper in front of you to write down...

Either ride or die or snitch. Now we have characterized my options. All right, let me think. All right, I've picked. Okay. I wrote it down on a piece of paper. And I have circled my choice. Okay, let's reveal to each other in three, two, one. Oh, you snitched on me. Oh, you went ride or die. Keith Romer? Ride or die, we are friends. What is this? Oh, Amanda. Oh, come on. So, great news for me.

I get to keep all of the money from Alex Goldmark. I don't have to Venmo anything. But if you could go ahead and open up your Venmo account right now. Yeah. Do I really have to do this? Yeah. $100. I'm running for stupid game organized by stupid Keith Romer. All right. There. Wow.

I'm not sure I want to keep working on this episode. Let's let the feelings simmer down and let's look at this through the lens of game theory. Fine. Emily Blanchard says, according to game theory, one of us played the optimal strategy. And one of us thought they were being a good person and your friend. Okay, whatever. The classic prisoner's dilemma, it's pure strategy. It's nobody cooperates with each other. Everybody steps on everybody else's toes. Which, Amanda, you will remember is what...

I did, but not what you did, right? Because I knew that if you, like, weren't loyal to me, I was risking sending Alex $100. Whereas if I ratted you out, the worst that could happen to me is that I have to send him $30. Or, in this case, because you're a nice Canadian, I sent zero dollars. And you should have known that about me, theoretically, in game theory. So...

Amanda, if we can, let's bring the game back from Keith and Amanda to the U.S. and China. Fine, whatever. Emily says there is one very important difference between the version of the game you and I just played. and the one she thinks the U.S. and China are playing where they have to decide whether or not to cooperate with each other.

And that difference comes down to the fact that the U.S. and China are not just playing this game once against each other. They are playing it over and over, day after day, month after month, year after year. It's a game that goes on forever. So once you go through stage, you know, well, we'll call it the 2025 version of the game, next you have the 2026 version of the game and the 2027 version of the game.

And game theory solves the game in a very different way when the game never ends. When you move to a repeated game structure, then you've got a threat, right? Which is not only will I not cooperate with you today. I will not cooperate with you forever. You do something nasty and act in your naked self-interest at my expense. I'm going to punish you for the rest of all time. But if one of us acted like a good person who was friends.

with the other person, and then the other meaner person followed that good person's lead, both of them would be better off than if we just kept doing mean-spirited things back and forth, Keith. I see what you did there. And that is why, for Trade Economist, The Prisoner's Dilemma is basically a game about cooperation.

So you think about large countries and, you know, there's a win-win where we have low tariffs with each other and a lose-lose where we're both putting high tariffs on each other. And so that? Maybe is what happened when Treasury Secretary Scott Besant went to meet those Chinese officials in Geneva. I think that's basically what they said in Switzerland.

This is kind of a lose-lose. Could we put these tariffs on pause while we find a better way to get to maybe not a win-win, but a lose-less, lose-less? So, reasonable approach. But that still leaves the puzzle of why the White House took this incredibly disruptive, month-long trade war roundtrip in the first place, from... 30% tariffs on China to 145% tariffs and then back down to 30% again, or whatever the courts ultimately say Trump can legally do. If on April 1st...

The Trump administration had said, so what we're going to do, we're going to threaten to raise tariffs really, really high. And actually, we're going to do it. We're going to make those tariffs crazy high against China. And then they're going to hit us back with their crazy high tariffs.

Then bond markets are going to lose their minds and do some pretty scary stuff. And then we're going to lower the tariffs against everybody else. And then we're going to lower the tariffs against China, bringing us back to where we started. That seems like a thing that if you had perfect foresight, you wouldn't do it all to begin with. And why did it play out this way? Emily has a few theories.

Theory one, maybe the administration really did think it was playing an ultimatum game and eventually figured out that no, it didn't in fact have all the power. Or theory two, Maybe the U.S. did think they were playing a prisoner's dilemma, but they just underestimated what the penalties were for starting a trade war with China. Maybe you don't really know what the costs of an action are for you.

So you've got to guess. I think tariffs would be actually not that bad for us. And then you impose tariffs and you get a whole bunch of phone calls from American companies saying these are terrible. And then... There is Emily's third theory that says that maybe neither side is even necessarily trying to win the tariff game at all. That the tariff game is just one tiny piece of this much, much larger metagame between the U.S. and China.

You might say, well, we're just talking about tariffs right now. Maybe. Or is it trade policy more generally? And then you can back up a little bit further. Is this about trade policy at all? And then it goes from economics to just non-economics. It could go very quickly to geopolitical competition. So there you are.

Which means the puzzle of figuring out what game is being played and what the payoffs are and what the best strategy is supposed to be, that puzzle is just exponentially more... Complicated. It's games within games within games. It's games all the way down. All the way down. Meanwhile, in the tariff game, we've got 74 days left in the latest round, that 90-day pause on the huge U.S.-China tariffs. 74 days for the two countries to decide what moves they want to make next.

If you would like to hear more about the US-China trade war, we've got recent episodes about how small businesses are dealing with the uncertainty created by this trade war. farmers' experiences of the last trade war, and a show that tries to get to the bottom of what made in China really means legally. You can find links for all of those episodes in our show notes.

Today's show was produced by Sam Yellow Horse Kessler with help from Sylvie Douglas. It was edited by Jess Jang, fact-checked by Sierra Juarez, and engineered by Kwesi Lee with help from Robert Rodriguez and Sina Lafredo. Alex Goldmark is our executive producer. I'm Amanda Aronchik. And I'm Keith Romer. This is NPR. Thanks for listening.