The Minimax Brink

Game Theory and Credible Commitment in October 1962

At 11:00 a.m. on Tuesday, October 16, 1962, inside the Cabinet Room of the White House, President John F. Kennedy leaned over a metal easel displaying black-and-white reconnaissance photographs taken two days earlier by Major Richard Heyser from a U-2 spy plane at 72,500 feet over San Cristóbal in western Cuba. Looking through a stereoscope, Air Force briefers pointed out erector launchers, oxidizer trucks, and four launch pads for Soviet R-12 (SS-4 Sandal) medium-range ballistic missiles. Equipped with one-megaton thermonuclear warheads and a range of 1,100 nautical miles, the missiles could obliterate Washington, D.C., or New York in less than thirteen minutes.

Throughout that first week of deliberations by the Executive Committee of the National Security Council (ExComm), the Joint Chiefs of Staff—led by Air Force Chief of Staff General Curtis LeMay—pressed Kennedy for an immediate military strike: 500 fighter-bomber sorties against the Cuban missile sites, followed within seven days by an amphibious invasion of 140,000 American troops. When Kennedy asked what Soviet Premier Nikita Khrushchev would do after hundreds of uniformed Soviet technicians in Cuba were killed by American bombs, LeMay replied that the Soviets would do nothing. Kennedy rejected that premise immediately, telling his brother Robert that the generals were ignoring the second move of the game: if the United States bombed Soviet forces in Cuba, Khrushchev would be forced by Politburo pressure to seize West Berlin, triggering a NATO nuclear exchange.

Thirty-six years earlier, on December 7, 1926, Hungarian mathematician John von Neumann had presented a paper to the Göttingen Mathematical Society—published in Mathematische Annalen in 1928 as Zur Theorie der Gesellschaftsspiele—that established the mathematical foundation for analyzing conflict against an intelligent adversary. In a two-person zero-sum game where Player 1 chooses a strategy distribution $x \in X$ and Player 2 chooses a strategy distribution $y \in Y$ over a payoff matrix $A$, von Neumann proved the Minimax Theorem:

In a zero-sum contest, a rational strategist cannot choose an action by hoping the opponent will make a mistake; one must assume the adversary will respond with the move that minimizes one's payoff, and therefore select the strategy that maximizes one's minimum guaranteed outcome.

By the late 1950s, however, as thermonuclear arsenals grew to thousands of megatons, the Harvard economist and RAND strategist Thomas C. Schelling recognized that nuclear crises were not zero-sum parlor games; both sides could lose everything simultaneously in mutual annihilation. In his 1960 book The Strategy of Conflict, which Kennedy had discussed with National Security Advisor McGeorge Bundy prior to the crisis, Schelling demonstrated that non-zero-sum bargaining under the shadow of catastrophe is governed by two mechanisms: focal points (unambiguous boundaries where expectations converge) and the manipulation of shared risk (designing small, reversible steps that place the burden of the final escalation onto the opponent).

Inside the Cabinet Room on October 18 and 19, Secretary of Defense Robert McNamara and Ambassador Llewellyn Thompson constructed an architecture drawn from Schelling's framework: a naval "quarantine" of offensive weapons shipments bound for Cuba:

• * Transferring the Escalation Trigger: An immediate air strike was an irreversible one-way door that killed Soviet soldiers at minute one and forced Khrushchev to retaliate in Berlin. By drawing a ring of 180 U.S. Navy warships 500 miles off Cuba—shortened on October 23 at the advice of British Ambassador David Ormsby-Gore to give Khrushchev twelve extra hours to think—Kennedy took the visible first step while leaving the decision to fire the first shot up to the Soviet captains approaching the line.
• * Creating a Salient Focal Point: The quarantine applied strictly to offensive missiles and bombers, allowing oil tankers and food ships to pass after inspection, creating a crisp boundary on the Atlantic.
• * Preserving a Golden Bridge for Retreat: On the evening of October 26, Kennedy received a personal cable from Khrushchev offering to dismantle the Cuban missiles in exchange for a public U.S. pledge never to invade Cuba. The next morning, Saturday, October 27—when a Soviet surface-to-air missile battery in Banes, Cuba, shot down and killed U-2 pilot Major Rudolf Anderson—a second broadcast arrived from Moscow demanding the public removal of fifteen American Jupiter nuclear missiles stationed in Turkey.

Rather than rejecting the second letter and ordering Monday's air strikes, Robert Kennedy and speechwriter Ted Sorensen executed the "Trollope Ploy": President Kennedy publicly ignored the second demand, formally accepted Khrushchev's Friday cable, and dispatched Robert Kennedy to meet Soviet Ambassador Anatoly Dobrynin privately at the Justice Department at 7:45 p.m. on October 27. There, Robert Kennedy delivered an unrecorded assurance that the obsolete Turkish Jupiter missiles would be dismantled within five months once the crisis ended—provided Moscow never mentioned the link publicly. At 10:24 a.m. on October 28, fourteen Soviet ships carrying missile equipment halted along the 500-mile quarantine line, and Radio Moscow broadcast Khrushchev's order to crate the thirty-six SS-4 missiles in Cuba and ship them back to the Soviet Union.