Crackhead’s Dilemma

The ‘Crackheads Dilemma’

So the ‘Prisoner’s Dilemma’ was first postulated by…. It DOESN’T matter, because you all already understand it intuitively. The scenario goes something like this: two ‘crackheads’ get caught robbing a pharmacy, they break in through the roof and hilariously can’t climb back out, like so. Now, what these two muttonheads don’t know is that there is a corpse in the back room, the owner had killed his wife and bounced just before they broke in.

At the station, the cops wanted to do as little work as possible and came up with this revolutionary idea. They know the criminals are getting done for breaking and entering but have no evidence that they killed the lady so Cop 1, lets call him Melvin Dresher, decides the criminals should be interrogated separately so that they cannot confer and prepare a strategy. The cops interrogate them simultaneously (in separate rooms) and offer them a deal to say the other guy killed the lady and receive a reduced sentence. Melvin thinks that any ‘rational agent’ would take the deal. He models the situation like so.

Screen Shot 2015-09-01 at 18.48.35Melvin- “These guys seem like rational individuals

Partner- “ Pfff OK, did you see the video bro!?”( see Gary Becker )

Melvin’s logic isn’t too bad:

In Box 1 they are each accusing the other of murdering the lady so there is a good chance at least one of them goes down for murder (2)

In Boxes 2 and 3 one guy says nothing and the other accuses him of murder, the backstabber does a few months in prison and goes free (0), the scapegoat goes down for life (3)

In Box 4 they both keep quiet, allowing for the possibility of the police actually doing their job, they still have a chance of doing a large sentence (1).

Melvin Dresher et al thought that for rational individuals the dominant strategy was to accuse your friend of the crime, all you have to do is consider the situation from one crackheads perspective. His options when the other guy sells out are: sell out=2, say nothing=3, if his counterpart is not going to sell out his options are sell out=0, say nothing=1. The dilemma is that when you are considering saying nothing in either situation you can  move down in terms of misery, either from 3 to 2 or 1 to 0 by changing your choice to ‘sell out’. There is an incentive for these guys to move from their position of being loyal to selling out.

Clearly, assuming criminals are ‘rational-agents’ is a flaw. Furthermore people try to change the outcomes in the boxes in all kinds of creative ways. Gangs for example, try to make the ‘Sell Out’ option seem much worse by threatening to murder your entire family. This effectively turns the 0’s in boxes 2 and 3 into… a 10? It isn’t easy stuff to quantify. It turns out that the crackheads in question loved each other, more so even than crack itself. They end up doing 2 years, together, successfully avoiding getting sexually harassed and working in department stores happily ever after.

The important thing to take from the Prisoner’s Dilemma is that people may end up hurting themselves while, counter-intuitively only thinking about themselves. The thing to take from the crack-head story is that in reality people’s welfare is linked intimately and by building a reputation of trust people can overcome the Prisoner’s Dilemma. We see it all the time.