Why game theory could be critical in a nuclear war

“Humanity’s half-life is approximately 35 years,” stated Nobel laureate in physics David Gross at the conclusion of his lecture during the German Physical Society’s conference in Erlangen in March. In other words, Gross suggests there is a 50 percent probability that humans could face extinction in just over three decades.

Gross’s concerning assertion came as he estimated that the likelihood of nuclear war is rising from 1 percent to about 2 percent annually. The audience left the lecture in deep thought, as the global situation and Gross’s grave warnings loomed heavily over them.

“I’m still hoping game theory will come to the rescue,” remarked another physicist at the conference. The logic proposed by game theory, assuming it is universally adhered to, could prevent a nuclear first strike.

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Reflecting on history, I find it challenging to be as optimistic. Rational behavior is uncommon. The creator of game theory, Hungarian-American mathematician and physicist John von Neumann, not only contributed to the development of the atomic bomb but also assisted in planning the U.S. nuclear attacks on Japan. He even advocated for a preemptive strike against the Soviet Union. The 20th century demonstrates that while game theory is an exceptional problem-solving tool, it doesn’t inherently ensure peace.

Game Theory Basics

Von Neumann significantly influenced numerous scientific domains in the 20th century, including information theory, quantum mechanics, and computer science. Contrary to the stereotype of introverted scientists, he was also known for hosting extravagant late-night parties.

His strategic thinking in various games led to the creation of his 1928 book Zur Theorie der Gesellschaftsspiele (“On the Theory of Board Games”), which attracted economist Oskar Morgenstern. Together, they compiled their insights on game strategies into the comprehensive book Theory of Games and Economic Behavior.

In game theory, different scenarios are evaluated and given numerical values, such as between –10 and 10, with higher values indicating more favorable situations for the player. The exact values are subjective, yet they enable objective strategy development.

To demonstrate game theory, imagine a chess game where player A decides between targeting a pawn on square 1 or another on square 2. Meanwhile, player B considers defensive responses. Game theorists assign numerical outcomes: if player A captures square 1 unchallenged, they receive +10 points, while player B gets –10. However, if player A captures square 1 but loses an important piece afterward, the score might be –4 for player A and +4 for player B.

Considering these scenarios can lead to decision-making loops. Player A anticipates player B’s actions, while player B anticipates player A’s awareness, potentially leading to endless cycles. Game theorists account for chance by proposing repeated scenarios to identify optimal strategies on average. Using a coin flip to represent opponent responses can help determine likely profitable actions. A “biased coin” may represent unequal odds favoring the opponent.

When Theorists Enter the War Room

Game theory extends beyond board games, aiding in scientifically informed decision-making and risk assessment.

In 1945, the U.S. aimed to prompt Japan’s swift surrender before Stalin’s intervention in World War II. The atomic bomb, shaped by von Neumann’s work, appeared suitable for this purpose. The U.S. needed a strategic plan, balancing military significance and surprise to thwart Japan’s preparations. Both nations, with limited resources, had to choose between defending and attacking cities. The U.S. considered Kokura, Hiroshima, Yokohama, Niigata, and Kyoto as targets.

Although the exact wartime decision-making process is unknown, von Neumann was on the committee that chose Hiroshima and Nagasaki as targets. Game theory likely played a role in these considerations.

Ultimately, Hiroshima and Nagasaki were bombed, resulting in approximately 200,000 deaths and achieving the U.S.’s objective as Japan surrendered.

Following World War II, the cold war commenced, marking the onset of the nuclear arms race between the U.S. and the Soviet Union. Von Neumann doubted a peaceful outcome, predicting an inevitable nuclear war, and supported a nuclear first strike. “If you say, why not bomb [the Russians] tomorrow, I say: Why not bomb them today? If you say today at 5 o’clock, I say why not 1 o’clock?” he reportedly stated in 1950.

Retrospectively, ignoring von Neumann’s advice against bombing the Soviet Union was wise, as the cold war ended without nuclear catastrophe.

Now, approximately 35 years post-cold war, the world faces renewed conflicts involving nuclear-armed nations. This context underscores the significance of the 2024 Mainau Declaration on nuclear weapons, spearheaded by Gross in reference to the 1955 Mainau Declaration and endorsed by over 100 Nobel laureates.

The declaration highlights the dire risk that these devastating weapons might be used “either by accident or by deliberate act,” potentially ending human civilization. Additionally, the first Nobel Laureate Assembly for Nuclear War Prevention issued a declaration with specific proposals to mitigate nuclear war risks, such as requiring at least two individuals to authorize a nuclear strike, which isn’t the case in some countries, including the U.S. and North Korea.

Let’s hope the scholars’ voices resonate, despite the bleak outlook.

This article originally appeared in Spektrum der Wissenschaft and was reproduced with permission. It was translated from the original German version with the assistance of artificial intelligence and reviewed by our editors.