The Washington PostDemocracy Dies in Darkness

What game theory tells us about nuclear war with North Korea

A man watches a news program showing photos published in North Korea's Rodong Sinmun newspaper of North Korea's “Pukguksong-2" missile launch at Seoul Railway station in Seoul.  (Ahn Young-joon/AP)

“Are we headed for a nuclear war?”

It’s the question hanging over, well, basically everyone these days, as North Korea flaunts new developments in its nuclear weapons program, threatening the United States, and President Trump promises “fire and fury” in response. Those tensions seem to be easing as of Wednesday, when Trump wrote on Twitter that "Kim Jong Un of North Korea made a very wise and well reasoned decision," possibly referencing a seeming pause in Pyongyang's anti-U.S. threats.

But the episode remains frightening, and it's all the more so because making predictions about nuclear war is deeply difficult. While history is full of case studies about what causes nation states to launch conventional war, the U.S. bombing of Hiroshima and Nagasaki are (thankfully) the lone examples of atomic attacks — and those were with weapons orders of magnitude less powerful than the current nuclear arsenal. That lack of historical precedent makes it hard for analysts to reason about nuclear conflicts and how to stop them.

That’s where game theory comes in. Game theory uses mathematical models to study conflict and cooperation between rational decision-makers.

“Game theory has been used to think about military issues since the beginning of the field in the 1940s,” said Tim Roughgarden, professor of computer science at Stanford University who focuses on game theoretic questions. He is the author, most recently, of “Twenty Lectures on Algorithmic Game Theory,” and won the Gödel Prize in 2012 for his work on routing traffic in large-scale communication networks to optimize performance of a congested network.

We spoke about how game theory can be used to help us understand war, nation states’ actions, and the current tension between the United States and North Korea.

This interview has edited for length and clarity.

Elizabeth Winkler: What is game theory?

Tim Roughgarden: Game theory is a field that involves reasoning mathematically about what happens when you have different actors who are strategic, who have different objectives, and what might happen when you have those actors in the same environment.

EW: Has it always been used to think about military strategy?

TR: The field has its roots in the 1920s. In some ways, there were mathematicians back then thinking about it in terms of poker and games of chance. But John von Neumann and Oskar Morgenstern’s book, “Theory of Games and Economic Behavior,” published in 1944, marked the birth of the field as an independent subject. Von Neumann also worked for U.S. think tanks in the context of Cold War strategy in the '40s and '50s, so game theory has really been used to think about military issues since the beginning of the field in the 1940s.

EW: How is game theory useful in understanding nuclear war?

TR: One thing game theory is useful for is providing very clean mathematical examples, parables almost, that help you articulate and reason about real-world situations in a logical way. They help you think through who the actors are, what their preferences are, which actions they can take and what possible outcomes could occur.

One of the most famous ones is the “Prisoner’s Dilemma.”  The story goes that there are two prisoners accused of a crime. Authorities put them in different rooms and interrogate them separately, so they can’t communicate with each other. The setup supposes that each can do one of two things: remain silent or betray their partner. If both remain silent, they both get a light jail sentence. If both betray the other, they each get more significant sentences. If one remains silent, and one betrays, the traitor goes free and the other gets a particularly stiff sentence. Each prisoner has every incentive to betray their colleague, even though the best outcome for them collectively is to both remain silent.

Nuclear war — to attack or not to attack — has a prisoner’s dilemma-like aspect to it. Each player has the opportunity to screw over the other. But there’s an important caveat: The prisoner’s dilemma assumes there is no future. If you’re just playing once, your dominant strategy would be to betray — or attack. But in a repeated prisoner’s dilemma, where players — say the U.S. and North Korea — are in long-term interactions, they’re reasoning not just about today but about the chances of retaliation tomorrow. In the presence of a credible threat of retaliation, now each country has an incentive to cooperate — to not attack. They act against their own interest in the short-term because it assures them no retaliation.

This is what happened with the U.S. and the Soviet Union during the Cold War. And this thinking was used as a way to reason about the stockpiling of nuclear weapons. Game theory can be used to provide one mathematical justification for the argument that nuclear buildup makes the world a more peaceful place.

EW: So are the U.S. and North Korea in a repeated prisoner’s dilemma?

To the extent that the scenario today with North Korea is analogous to that with the Soviet Union, the same parables that were helpful for thinking about strategy then could be helpful today as well. But the current situation has not quite reached a prisoner’s dilemma because North Korea doesn’t yet have a symmetric ability to retaliate against us as we do against them. They’re developing that ability so that the situation becomes a prisoner’s dilemma.

EW: How does game theory suggest the U.S. should act?

TR: There are situations where you apply game theory and it gives you crisp, clear prescriptions about what you should do. In principle you could use game theory to decide what is the best way of bluffing in a game like poker. But in real world applications it doesn’t always tell you what you should do. It can give you the possible outcomes, but it’s doesn’t give you a whole lot of advice about how you should guide things to the endgame you want.

Here’s another famous example: Imagine two people want to go out to dinner and there are two restaurants in town—one French, one Italian. The first order of preference for both people is to have dinner with each other, as opposed to eating alone. But one person prefers French and the other prefers Italian. So there are two possible endgames worth striving for — where both go to the French restaurant or both go to the Italian restaurant. But it’s not at all clear how you get there.

Game theory is very helpful, though, when you have a clear belief about what the other side is going to do. This is the notion of a “best response.” If you know that another country will bow to a threat rather than retaliate, then there’s a much stronger case for issuing a threat. If you don’t know how they’ll act, reasoning about a best response becomes much more difficult.

This is one aspect in the situation with North Korea that has everyone a bit on edge: Neither side has a very good understanding of the other. Kim is young, there’s not been much direct interaction between him and the U.S. government and not a lot of confidence in understanding how he might act in different situations. And given the things Trump has been saying, North Korea might not be sure how the U.S. will react either.