Sunday, September 13, 2009

The mysterious equilibrium of zombies - The Boston Globe:

In the final scenes of “The Dark Knight” (spoiler alert!), the Joker gives the following choice to the passengers of two ferries: they can either blow up the other boat and save themselves, or themselves be blown up. If no one decides within a certain amount of time, both ferries are destroyed.

The typical moviegoer pretty much thinks one thing: Batman better show up now. But the mathematician immediately recognizes the Joker’s trap as a variation on the classic problem of the prisoner’s dilemma, where two individuals, each isolated in a prison cell, are given a choice: betray their friend and go free, or cooperate by saying nothing, and be given a short prison sentence. If each betrays the other, however, they will get a longer prison sentence.

This seminal problem in game theory has an important property: while cooperation is a more socially beneficial strategy, it is actually a more “stable” strategy for each person to betray the other, since this makes each better off independent of the whims of his friend. This behavior is known as a Nash equilibrium and is named after John Nash, well-known from the more obviously mathematical film, “A Beautiful Mind.”