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Friday, April 11, 2014

Prisoner's dilemma on the road

Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of speaking to or exchanging messages with the other. The police admit they don't have enough evidence to convict the pair on the principal charge. They plan to sentence both to a year in prison on a lesser charge. Simultaneously, the police offer each prisoner a Faustian bargain. Each prisoner is given the opportunity either to betray the other, by testifying that the other committed the crime, or to cooperate with the other by remaining silent. Here's how it goes:

If A and B both betray the other, each of them serves 2 years in prison
If A betrays B but B remains silent, A will be set free and B will serve 3 years in prison (and vice versa)
If A and B both remain silent, both of them will only serve 1 year in prison (on the lesser charge)

It's implied that the prisoners will have no opportunity to reward or punish their partner other than the prison sentences they get, and that their decision won't affect their reputation in future. Because betraying a partner offers a greater reward than cooperating with them, all purely rational self-interested prisoners would betray the other, and so the only possible outcome for two purely rational prisoners is for them to betray each other. The interesting part of this result is that pursuing individual reward logically leads both of the prisoners to betray, when they would get a better reward if they both cooperated.
A six-lane highway narrows to a two lane highway as it approaches what Memphis residents refer to as Malfunction Junction. Sam Cooper Blvd to the west crosses I-240 and becomes I-40. (Isaac Hayes Memorial Highway) Driving home eastbound on Sam Cooper, during afternoon rush-hour is a nightmare. Along a one-mile stretch, the three east-bound lanes narrow to two, then to one. As I approach this one-mile-stretch, I notice that the cars are backed up for more than a mile in the far-left lane—which is inching along at less than a mile per hour. The reason that they're moving so slowly, is because cars from the right two lanes are driving as far as they can and then they're pushing their way into the far-left lane.
Click the picture to see more detail.

The left-lane is going really slow because of the commotion where vehicles in the far-left lane are forced to come to a complete stop because pushy and reckless middle and right-lane drivers are forcing their way into the left lane traffic in an asinine game of sideways chicken. Most of the cars in the right and the middle lane already know that this traffic situation has been going on for over a month and the DOT has announced it will continue for more than a year, as they build new exits, overpasses, and additional lanes.

Here is why I think of it as prisoner's dilemma. In order to save themselves a few minutes of time waiting in line, inconsiderate middle and right-lane drivers hold up the left-lane of traffic, causing a responsible left-lane driver who gets in line as is expected, to wait in that left-lane line for as long as thirty minutes. If everyone would get in line on the left as soon as possible—a mile before the narrows—then everyone would get through in less than ten-minutes. Unfortunately this never happens, because—as I've mentioned before—too many drivers are selfish pricks.

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