Game Theory & Nuclear Strategy

Game theory tends not to be the most popular class for many M1 Economics students. Mathematical formalism and rigorous logical arguments tend to scare or bore rather than engage. What makes game theory truly exciting, however, is its wide range of applications from evolution biology to political science. The discussion of military strategy during the Cold War was the crucial catalyst that brought game theory onto the stage in the first place. This article will give a historical overview of the development of nuclear strategy during the Cold War era and show parallels to game theoretic applications.

The beginnings of the Nuclear Race (1945-1949)

The US started the era of nuclear weapons on July 16th, 1945 with the first test of an operational nuclear warhead in the Nevada desert. A research team, labelled the “Manhattan Project”, succeeded in constructing a Uranium-based weapon of unprecedented destruction power. By that time, the war in Europe had already ended and President Truman was informed at the Potsdam conference of the successful test. The weapon was used against Japan in an attempt to end the war quickly and avoid a bloody invasion of the Japanese main islands. On August 6th, 1945, the first bomb was dropped on Hiroshima, and on August 9th a second bomb was dropped on Nagasaki, forcing Japan’s surrender. In Hiroshima alone, the bomb killed 50,000 people directly, another 100,000 indirectly and mutilated many more.

With the end of the war, the alliance between the US and the Soviet Union ended and old hostilities resurfaced. Consequently, in October 1945, the US drafted a contingency plan for defeating the Soviet Union with 20 more bombs, silently going over the fact that, at that point, no more bombs were available. In fact, such a report testified to the lack of nuclear strategy within the US: there was no understanding of the needs and capabilities of the nuclear bomb in the current situation and no directives under which circumstances to use it, short of a direct attack on the United States. The bomb was mainly considered a new means of strategic bombardment. This started the first phase of the Cold War: the US monopoly on nuclear weapons.

The Soviets catch-on (1949-1962)

When the Soviets finally gained the weapon in 1949, they considered it as catch-up in terms of firepower. Only after Stalin’s death in 1953 did they think about using it in dramatically new ways. At the same time, the development of the Hydrogen bomb (“H-Bomb”) increased the threat nuclear weapons posed, for this new bomb constituted a massive step-up in firepower: even a miss of many miles would destroy a city. By 1954, both sides had it, but the US retained one critical advantage: a monopoly on the means of delivery, including a large fleet of strategic bombers and air bases circling the Soviet Union – especially in Turkey, which became a NATO member in 1952.

Politically, this time saw a further deterioration in US-Soviet relations: the Berlin Blockade between 1948 and 1949 or the Korean War (1950-1953). The result of these international crises was the formulation of a first coherent nuclear doctrine for the US under the Eisenhower administration. In early 1954, Secretary of State J.F. Dulles outlined the following strategy: if the Soviets or their allies acted aggressively in any part of the world, the result may be a full-scale nuclear attack against the Soviet Union. From a game theory point of view, this is exactly a “grim trigger” strategy: Even the slightest deviation from mutual cooperation (here, not behaving aggressively) would be met with the maximum possible punishment. In non-cooperative game theory, this is considered one of the most effective ways of enforcing cooperation between players. In Cold War terms, this was called the Doctrine of Massive Retaliation. This was considered a lesson from the Korean War, which Michael Nacht (University of Berkeley) formulated as: “Why fight limited wars? Why fight the communists on their own terms? Why don’t we use our advantages, our assets? And they felt, and Dulles, in particular, felt that our main asset was still a superiority in nuclear weapons.” In fact, the rush for nuclear capabilities was extraordinary: on the US side, the arsenal was propped up from 50 warheads in 1948 to more than 7,000 warheads in the mid-50s. The B-52 bomber with a range of 7,652 nautical miles, could reach deep into Soviet territory while other short-range bombers in Europe added to the US delivery capacities (circa 2000 bombers in total).

By 1955, the Soviet Union had developed their first strategic bomber and had the only three available planes flying over a military parade several times, tricking the West into believing that they had many of them. In 1957 the Soviets succeeded in launching mankind’s first satellite, Sputnik, surprising every observer with the advanced state of Soviet space and missile technology. The American public began to fear a Soviet first strike, believing more and more in the technological superiority of the Soviet Union. The success of Sputnik gave Khrushchev the political power to shift resources from bomber production to missile nuclear warfare. The US reacted to this perceived “missile gap” with a speeded up missile programme, encircling the Soviet Union with medium range missiles in Italy and Turkey by the late 50s. The situation was now that hardened concrete silos spread all over those countries stood ready for launch in case of a nuclear conflict.

From a strategic point of view, Sputnik devalued Massive Retaliation: if both countries had delivery capacities, it was not credible to react to, say, a small incursion in a third-world country with a nuclear strike on the enemy’s home territory. The new strategic doctrine employed by NATO was called Flexible Response and its idea was to respond in a commensurate way to the scale of the aggression. Robert McNamara (former Secretary of Defense) said: “We proposed Flexible Response with a very high threshold meaning that we could hardly conceive circumstances in which NATO could benefit by initiating the use of nuclear weapons.” The strategy was put to test for the first time during the Cuban Missile Crisis (1962). When the Soviet Union was found to be building up nuclear delivery capacities in Cuba, only 90 miles from Florida, the US were directly threatened by nuclear weapons for the first time. The use of a nuclear strategy in the event of a crisis, such as the Cuban Missile Crisis, was to guide policy makers and reduce the potentially fatal uncertainty of the adversary about the US’ threshold to use nuclear weapons. McNamara later denied that a US first strike was ever seriously considered as an option; however, the risk of an unauthorised or accidental launch of nuclear weapons was possible. After a 13-day standoff between US president Kennedy and Soviet leader Khrushchev, the Soviets were forced to withdraw missiles.

The MAD times and the SALT agreements (1962-1979)

By the mid 60’s, the Soviets had finished the deployment of ICBMs (Intercontinental Ballistic Missiles) and cemented the new reality of the nuclear standoff: Mutually Assured Destruction. (Kudos for the fitting acronym MAD go to the black humour of game theorist and mathematician John von Neumann). With both adversaries capable of delivering a deadly blow, starting a nuclear war was sure to escalate into a global apocalypse, no matter who started or put himself into an advantageous position. Game theoretically speaking, imagine a perverted prisoner’s dilemma, in which each deviation results in extermination (Table 1):

Table 1: Massive retaliation gives no player a benefit from aggressive behaviour.

US/USSR Deterrence Defect
Deterrence (1,1) (-∞,-∞)
Defect (-∞,-∞) (-∞,-∞)

Deterrence became the new strategic imperative, credibly signalling one’s capability for a second strike after having suffered a hostile first strike was the key to keeping the balance. In the US, a three stage system, the “Triad”, was employed to guarantee these capabilities: Some B-54 strategic bombers were held ready permanently with a modernised fleet of 600 intercontinental bombers; constantly moving Polaris nuke-carrying submarines were hidden in the ocean; and the “Minuteman” land-based missile in hardened-concrete silos as the ground component to this nuclear system. The Soviets had technical problems with bombers and submarines, which severely limited their possibility to use these weapons with great precision, so ICBMs were still the most reliable option for them. The Soviets also enjoyed the strategic advantage of a huge landmass to hide silos and stretch them out. No matter the technical limitations, Mutually Assured Destruction was a fact of life in the second half of the Cold War, from which there was seemingly no escape.

The Strategic Arms Limitation Talks (SALT I in 1972, SALT II in 1979) stabilised the relations in the MAD-environment. According to Professor Nacht, for economic as well as political reasons, the US were interested in arms control instead of an arms race. SALT I limited the maximum number of different systems and introduced means to verify them. Also, it started defining stabilizing and destabilizing weapons: which ones were desirable to have and which ones were dangerous? The rationale behind this seemingly paradoxical distinction was based on which weapons seemed to threaten a first strike. If the US introduced weapons that gave the Soviets the impression that they were able to annihilate the Soviet Union and render them incapable of retaliation, the Soviets might choose to launch the first strike to pre-empt such a strike. That was the nature of destabilizing weapons: small, short range weapons that were easy to conceal and mostly useful for a possible first strike.

As the available weapons increased in quality and precision, nuclear strategists went from the notion of Counter-Value targeting (targeting cities, which did not require precision) to Counterforce (targeting adversary’s forces, which required precision to disarm the opponent). The goal was effective deterrence of strategic warfare. NATO considered it as an extension of flexible response with the goal of striking limited, precise attacks to counter other limited attacks.

Carter and Brezhnev signed the 2nd SALT agreement in 1979, allowing the Soviets to maintain a greater number of large land-based weapons while the US got higher ceilings for some other weapons. Both sides developed counterforce capabilities. The Carter administration was still afraid: they introduced the MX missile system as a political response to show they were also still expanding capabilities. The MX was a premier counterforce weapon: it was very precise and reliable and under the logic of SALT a desirable weapon, even if it made some strategists nervous.

President Carter also commissioned Pershing-II, a precision guidance weapon stationed in Europe able to reach targets in the Soviet Union in 5 minutes. Within the Reagan administration, Secretary of Defence Caspar Weinberger welcomed them, as he saw the US falling behind. Like him, most American officials were worried about the Soviets, who kept upgrading their capabilities. As a consequence, the 80s saw very large step-ups in the defence budgets. Erring on the side of caution adds to an arms race and a huge number of weapons abound continue to be a danger to the world.

This brief overview of the development of nuclear strategy during the Cold War shows that a solid game theoretical understanding, but also a healthy scepticism about the limits of human rationality, are important to keep the balance and preserve peace.

This article is partly based on the Heroes vs. Traders article “A Short History of Nuclear Strategy – Part I” by the same author. See and follow for more geostrategical and game theoretical analysis.

by Philip Hanspach

Further references:

Powell, Robert. Nuclear deterrence theory: The search for credibility. Cambridge University Press, 1990.

Field, Alexander J. “Schelling, von Neumann, and the Event that Didn’t Occur.” Available at SSRN 1095946 (2013).

Leonard, Robert J. “From parlor games to social science: von Neumann, Morgenstern, and the creation of game theory 1928-1944.” Journal of Economic Literature (1995): 730-761.

Philip’s game corner 1: Balance of Power (1985): This original Cold War relic is available for free online if you can make Windows 3 run on a DOSBox. The tricky installation is worth your while as the New York Times Sunday Magazine writes “Balance of Power is about as close as one might get to the cut-and-thrust of international politics without going through confirmation by the Senate”. Engage in bargaining games over international crises to avoid nuclear war, which would result in a mutual game over, while preserving your sphere of influence to increase your geopolitical prestige.

Philip’s game corner 2: Defcon (2006): Had enough of preventing nuclear war? In this unconventional strategy game, you command the strategic assets of a continent and have to defeat the opponent by nuking his cities using land-based silos, bombers and submarines. Can you out-guess your opponents or lead alliances to lose less than your enemy? Very simple to learn, but with incredible strategic depth and engaging atmosphere and presentation.