GAME THEORY & THE CUBAN MISSILE CRISIS

What is Game Theory?• A branch of mathematics concerned with decision-making

in social interactions.• Games = situations• Players = participants• Strategies = possible actions

• Nash Equilibrium: combination of two strategies from the players that are “stable”, in that neither player can do better

Cuban Missile Crisis Strategies

United States

1. Naval Blockade (B) – prevent shipment of more missiles, possibly followed by stronger action to induce USSR to withdraw missiles already installed

2. Air Strike (A) – wipe out missiles already installed, possibly followed by invasion of the island

Soviet Union

3. Withdrawal (W) – remove their missiles

4. Maintenance (M) – maintain their missiles

Compromise(3,3)

Soviet VictoryU.S. Defeat

(2,4)

U.S. VictorySoviet Defeat

(4.2)

Nuclear War (1,1)

Withdrawal (W) Maintenance (M)

Soviet Union

Blockade (B)

Air Strike (A)

Un

ited

Sta

tes

Key(x,y) = (payoff to U.S., payoff to USSR)4=best, 3=next best, 2=next worst, 1=worst

Prisoner’s Dilemma• Two suspects are arrested by the police. The police have

insufficient evidence for a conviction, and, having separated the prisoners, visit each of them to offer the same deal. If one testifies for the prosecution against the other and the other remains silent, the talker goes free and the silent accomplice receives the full one-year sentence. If both remain silent, both prisoners are sentenced to only one month in jail for a minor charge. If each betrays the other, each receives a three-month sentence. Each prisoner must choose to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation. How should the prisoners act?

Each serves 1 month(3,3)

A serves 1 yearB goes free

(1, 4)

A goes freeB serves 1 year

(4,1)

Each serves 3 months

(2,2)

Remain Silent Talk

Remain Silent

Talk

Pri

son

er A

Prisoner B