Game Theory: Tit for Tat

Here's a great explanation from the TV show NUMB3RS of the tit-for-tat strategy in an iterated prisoner's dilemma game.

Tit for tat is a highly effective strategy in game theory for the iterated prisoner's dilemma. It was first introduced by Anatol Rapoport in Robert Axelrod's two tournaments, held around 1980. Based on the English saying meaning "equivalent retaliation" ("tit for tat"), an agent using this strategy will initially cooperate, then respond in kind to an opponent's previous action. If the opponent previously was cooperative, the agent is cooperative. If not, the agent is not. This is similar to reciprocal altruism in biology.

Here is the basic set-up for the prisoner's dilemma game. Notice that regardless of what the other prisoner does, each prisoner is better off betraying the other rather than staying silent, even though their optimal cooperative strategy would be for both to stay silent. (Hence the dilemma.)

	Prisoner B Stays Silent	Prisoner B Betrays
Prisoner A Stays Silent	Each serves six months	Prisoner A serves ten years Prisoner B goes free
Prisoner A Betrays	Prisoner A goes free Prisoner B serves ten years	Each serves five years

The prisoner's dilemma has many applications in the analysis of economics, law, biology, politics, etc. It's ubiquity is what makes it such an interesting thing to study.

From what little I've seen of it, NUMB3RS is an excellent show. As a former math teacher, it is great seeing a show like this popularizing many of the cooler aspects and applications of various branches of mathematics.