The Prisoners’ Dilemma
In the prisoners’ dilemma game (PDG) the prisoners, who are unable to communicate, can still choose to cooperate—or defect. The game is rigged so that each is better of if they personally defect, no matter what the other does.
So IF they are sociopathic, and do not care at all what happens to the other, their only logical choice is to defect. But in this game that makes them worse off than if both cooperated. Economic (sociopathic) preferences plus logic, prevent cooperation.
The Climate Connection
International climate negotiations are essentially a PDG with many prisoners instead of just two. They can, however, talk to each other. But after they do, and make their nice promises, they can still do what they want. And they are still better off defecting (doing nothing) than cooperating, no matter what the others do.
One hope for cooperation (and the one I plan to soon test experimentally) is that when the same players play the same game over and over, they will learn to cooperate. In the two-player PDG, this often happens for a while, so there is hope. With a larger group, cooperation starts out at about half the level that would be best and then deteriorates fairly rapidly. I will be looking for a way to improve this behavior, without targetted enforcement.
Repeated (Super) Games
Standard game theory draws a dismal conclusion. No matter how many times two players play the same PDG, they will never cooperate even once.
The “proof” is called backward induction. (1) The last time they play, they can do nothing to encourage future cooperation, so they both defect. (2) In the next-to-last game, they can do nothing to encourage future cooperation because they know, by step #1, that they will defect in the last game. (3) in the 3rd to last game … well you get the drift. They are doomed.
In the pages below this one, I will take on this proof, and show that mathematically (due to some hidden assumptions) it’s true. But the hidden assumptions are completely ridiculous with regard to humans. Scientifically speaking, there is no proof of this dismal result.
Just to satisfy curiosity, the hidden assumptions are:
- Player A knows that player B is a sociopath. And knows that player B knows that A is a sociopath and knows that B knows A knows B is … forever. And the same for player B.
- Both players will believe in backward induction so strongly that they never as what would happen if they cooperated and thereby proved to the other that assumption #1 was wrong.
What Use Is This?
Mostly, this is a lesson in how standard game theory is not scientific and why we should pay attention to behavioral game theory that provides a path to a scientific theory.
It may also help us think more clearly about the climate game because it shows that what brings about cooperation is the possibility that there are non-sociopathic players. And it even shows that if the players in the game are true sociopaths, they may still cooperate if they are not sure that the others are all true sociopaths. So having some non-sociopathic countries in the mix is crucial, but their role can be simply to make it credible for sociopaths to claim they are not sociopaths.
While this insight is interesting, it may not be very important for designing a good approach to cooperation.