June 02, 2012
A Dirty Twist on Beating the Prisoner's Dilemma
Michael Marshall in New Scientist:
In the prisoner's dilemma, if both players keep quiet, each gets a brief sentence. But if one betrays the other, the snitch gets off scot-free while their partner suffers a long sentence. If both players betray each other, each gets a medium sentence. As a united pair, players do better if they both keep shtum. But crucially, if criminal A thinks B won't blab, it is in A's best interest to snitch, as he will then walk free - at B's expense.
The dilemma has obsessed economists for over 50 years because it helps to explain why individuals sometimes don't cooperate even when it is in their combined best interests to do so. Even climate change negotiations can be thought of as a prisoner's dilemma: no country wants to pay the cost of cutting emissions (keep shtum) if everyone else is going to keep on emitting (snitch).
The game becomes interesting when the same two partners play it over and over again. The way to minimise jail time under these conditions is usually to "play nice": don't snitch, on the assumption that your partner won't either, and if they betray you then snitch on them in the next round, as a warning. So essentially, the best strategy is to collaborate.
Now, William Press at the University of Texas at Austin says he has uncovered a strategy to win that is not collaborative. And players who adopt his strategy end up spending much less time in prison than their opponents - in collaborative games, both players end up spending roughly equal time in prison.
Posted by Robin Varghese at 12:49 PM | Permalink
Comments
"Even climate change negotiations can be thought of as a prisoner's dilemma: no country wants to pay the cost of cutting emissions (keep shtum) if everyone else is going to keep on emitting (snitch)."
This analogy breaks down because the negotiation is not taking place with the environment, which cannot negotiate.
It can only be left alone in a healthy condition, in which case civilization continues.
Or it can be polluted to the point of ecocide, in which case civilization goes down.
It is an illusion for nations to think their negotiations can change reality.
North Carolina lawmakers provide one glaring example.
Posted by: Dredd | Jun 2, 2012 4:38:47 PM
As Daniel Ellsberg no slouch at game theory himself said long ago: the prisoners dilemma is the logic of torturers.
Posted by: blavag | Jun 2, 2012 5:09:02 PM
If I understand it, the strategy is to play nice initially and wait for the opponent to defect first. If/when that happens, retaliate disproportionately until the opponent recognizes that they won't come out ahead in the end by defecting because the other party will always respond this way, so they cooperate going forward.
This is, of course, the strategy employed around the world by children and adults in all kinds of contexts, so I had to search for what was novel about the result.
Only two things appeared as candidates: it uses mathematics and turns common intuition into proof, and it assumes both parties have a theory of mind. If this truly is a novel development in game theory, what a sad commentary that it took so long to arrive.
Posted by: Jonathan Halvorson | Jun 3, 2012 9:49:00 PM
Jonathan, I think Carl Sagan wrote about this as "The Brazen Rule," a long time ago, obviously. And -- do both players need a theory of mind for game theory to bind them? Does it not have to work whether one accepts it or understands it or "believes in" it? I agree with you -- this is not uplifting stuff....
Posted by: Elatia Harris | Jun 3, 2012 10:47:58 PM
I didn't read the entire original paper, so by "theory of mind" I took them to be saying that retaliating was understood to be a deliberate effort to make sure that the defector would not profit in the long run by defecting. Since in the iterated prisoner's dilemma scenario you have the ability to make good on this intention, once it's conveyed it has a long-term impact on bringing cooperation. But you have to understand the point of the action to change behavior.
Now, do you really need a theory of mind to get cooperative behavior? You can program machines to mimic cooperative behavior and "learn" from past patterns to engage reliable cooperation eventually without it. Maybe the point is that a theory of mind makes the learning process to arrive at cooperation more efficient, thus producing a better score.
Posted by: Jonathan Halvorson | Jun 3, 2012 11:33:14 PM
Thank you, Jonathan -- I appreciate it. If a machine can be programmed to beat Kasparov, then I suppose it could be programmed as you say. But isn't the point of either cooperating or backing the other guy down that something must be at stake? Otherwise these theories have the worth of perpetual motion machines.
Posted by: Elatia Harris | Jun 4, 2012 12:29:55 AM
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