“The half-life of humanity is currently around 35 years,” said Nobel laureate in physics David Gross as he concluded an evening lecture at the German Physical Society’s conference in Erlangen in March. Put another way, the physicist believes that in a little more than three decades, there is a 50 percent chance that our species will be extinct.

The alarming statement followed Gross’s estimation that the risk of a nuclear war was increasing from 1 percent per year to about 2 percent annually. After the lecture, the audience was visibly pensive. The current world situation and the award-winning speaker’s warnings hung over attendees like a dark cloud.

“I’m still hoping game theory will come to the rescue,” another physicist later told me at the conference. The rules of logic—provided everyone follows them—would prohibit a nuclear first strike, this reasoning goes.

But looking at history, I’m not quite so optimistic. Unfortunately, people rarely act rationally. Furthermore, the founder of game theory, the brilliant Hungarian-American mathematician and physicist John von Neumann, not only helped develop the first atomic bomb but also worked with the U.S. government to plan the nuclear attacks on Japan. He even recommended a preemptive strike against the Soviet Union. The 20th century reveals that game theory offers a remarkable tool for problem-solving, but it does not, in itself, guarantee peace.

Game Theory Basics
Von Neumann profoundly shaped numerous scientific fields in the 20th century, including information theory, quantum mechanics and computer science. He was also—contrary to stereotypes about introverted scientists—notorious for his wild late-night parties.

Thinking about strategy in various games would eventually lead to von Neumann’s 1928 book Zur Theorie der Gesellschaftsspiele (“On the Theory of Board Games”), which caught the attention of economist Oskar Morgenstern. The two researchers began compiling and publishing their joint reflections on game strategies, and this culminated in the nearly 700-page book Theory of Games and Economic Behavior.

In game theory, various scenarios are considered, and each is assigned a numerical value, for example, between –10 and 10. A high value symbolizes a particularly advantageous situation for a particular player. The exact numerical values chosen for each situation are subjective. Based on this subjective weighting, however, an optimal strategy can then be developed from an objective perspective.

For the purposes of illustrating how game theory can be applied, let’s consider a scenario where two players are, say, playing chess. Just to keep things simple, imagine that player A is weighing two moves: target a pawn on square 1 or a different pawn on square 2. The opponent, player B, is also thinking defensively about how to respond. Game theorists would assign different scenarios numeric outcomes. For example, if player A succeeds in taking square 1 with no negative consequences, they will receive +10 points, and player B would receive –10 points. If player A takes square 1 but immediately thereafter loses a valuable piece, then the outcome is –4 for player A and +4 for player B.

If you spend enough time thinking about these scenarios, you may notice that there’s a danger of getting trapped in a decision-making loop. For instance, player A knows that player B is likely to follow a particular course of action, but player B knows that player A knows that, too, and so might do the opposite. This little thought experiment turns into an unending spiral.

So one of the additional steps that game theorists take is leaning into the idea that chance will be part of the process. In cases where there is no optimal decision, to avoid the loop of “I know what you’re thinking but you know what I’m thinking,” game theorists propose imagining that a particular scenario will be repeated many times over. Then they ask which course of action is the best for a particular player on average. You could represent the opponent’s response using a coin flip, for example, to game out what’s likely to pay off. And you can stack the odds with a “biased coin” to explore the best strategy, assuming the odds are not 50–50 for a particular response but instead tilted more in your opponent’s favor than your own.

When Theorists Enter the War Room
But game theory is not just about board games. It’s about making scientifically sound decisions and weighing the associated risks.

For example, in 1945 the U.S. wanted to force Japan to surrender as quickly as possible, before Stalin could intervene in World War II. The U.S.’s new atomic bomb, whose development von Neumann had significantly influenced, seemed suitable for this purpose. Yet the U.S. needed a strategy for this weapon. On the one hand, the targets had to be important from a military perspective; on the other hand, they should not be too obvious, so as not to prevent Japan from preparing for the attack. Japan and the U.S. were each trying to stay one step ahead of the other. At the same time, both nations had finite resources and had to decide between attacking and defending individual cities. American strategists considered five different target cities: Kokura, Hiroshima, Yokohama, Niigata and Kyoto.