[philh]

> The Joker scares the city onto its two ferries. Once the ferries are in the middle of the water, he cuts their power and gives them both a button to blow up the other ferry, thereby constructing a prisoner’s dilemma (one boat is filled with real prisoners). The passengers discuss and vote. One of the prisoners makes a Ulysses pact and credibly commits by tossing the detonator overboard.

This isn't actually a prisoner's dilemma. In a PD, both players decide simultaneously, and your payoff depends on both choices. In this, your payoff simply depends on who defects first, with the caveat (which turns out to be false) that if nobody defects you both die.

(If you assume both boats decide simultaneously whether to defect or not, it still isn't a PD. The payoff matrix looks like 1,1 / 1,0 / 0,1 / 0,0 if nobody dies when they both cooperate: it's not a PD because defecting doesn't increase your score. If everyone dies when you both cooperate, the payoff matrix is 0,0 / 1,0 / 0,1 / 0,0: utility is not maximised by both players cooperating.)

Nor is tossing the detonator a credible commitment, in game theory terms, unless the other boat sees it.

[Roxolan]

It's actually more complicated than that. You value saving the lives of people on the other boat (albeit much less than you value your own), there are "third options" with risks but interesting payoffs that are worth considering (disabling the bomb, stealthily jumping into the water...), and the longer you delay, the more likely it is that a deus ex machina (Batman, a stealth bomb disposal specialist...) will show up and offer you maximum payoff on a silver platter. Indeed that's what ends up happening in the movie.

(Of course this isn't a practical approach, since the problem is likely to solve itself long before I'm done formalizing it.)