Game Theory & the cuban missile crisis

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Presentation transcript:

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 Naval Blockade (B) – prevent shipment of more missiles, possibly followed by stronger action to induce USSR to withdraw missiles already installed Air Strike (A) – wipe out missiles already installed, possibly followed by invasion of the island Soviet Union Withdrawal (W) – remove their missiles Maintenance (M) – maintain their missiles

Soviet Union Withdrawal (W) Maintenance (M) United States Compromise (3,3) Soviet Victory U.S. Defeat (2,4) U.S. Victory Soviet Defeat (4.2) Nuclear War (1,1) Blockade (B) Air Strike (A) 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?

Prisoner B Remain Silent Talk Prisoner A Each serves 1 month (3,3) A serves 1 year B goes free (1, 4) A goes free B serves 1 year (4,1) Each serves 3 months (2,2) Remain Silent Talk Rational choice leads both to talk, even though the individual reward would have been greater if they had both remained silent.