From dilemma to tragedy

In game theory, there’s an interesting problem called the prisoner’s dilemma. There were these 2 prisoners who were accomplices in a crime, but they didn’t know each other prior to the crime. They’ve been caught, and were individually questioned. Assuming no social consequences nor retributions, each prisoner was asked to confess to the crime.

If prisoner A confessed, but prisoner B kept quiet, A was let go and B was to take the full blame (and vice versa). If both confessed, both gets jailed, but less than if a single prisoner took the fall. Now, if both kept quiet, both still gets jailed, but for a significantly less amount of time than the previous situation.

Prisoner hands by Andrejs Zemdega
[image by Andrejs Zemdega]

The action “keeping quiet” corresponds to “cooperate”. The action “confess” corresponds to “defect”.

When I first learned of the concept, it was in the form of rewards, as opposed to punishment above. So here’s a table where the values correspond to rewards.

  A cooperate A defect
B cooperate A gets 0.8
B gets 0.8
A gets 1.0
B gets 0.0
B defect A gets 0.0
B gets 1.0
A gets 0.2
B gets 0.2

[the table might look a bit crushed together if you’re reading in a feed reader]

I made up the values. They’re meant to illustrate the disparity between the cases. You might also have heard of other versions of the prisoner’s dilemma. I want to highlight the part where both prisoners benefit more from cooperation than defection. The special case is if one chose to defect and the other chose to cooperate. But cooperative benefits are higher than an individual benefit.

When total selfishness comes into play, the selfish individual achieves the optimal benefit. But the optimal benefit isn’t much higher than the cooperative benefit. Being even a little less selfish creates a better outcome for all.

Now compare this with tragedy of the commons. A group of people have a shared finite resource. When everyone cooperates by taking only their fair share, all is well. When one person selfishly takes more than his fair share, the group on the whole suffers.

Since there’s no real incentive to be selfless at that point, more people might start taking more (defecting). And suddenly the finite resource gets abused and becomes useless.

For example, carbon footprints. Everyone wants to be environmentally friendly. When someone thinks there’s enough clean air for everybody, he might selfishly decide to up the noxious gas output (as a means of upping his profit too). If it comes to a “every man for himself” situation, the planet is going to be in deep trouble.

Economically speaking, there isn’t much relation between the prisoner’s dilemma and the tragedy of the commons. Socially speaking, in particular selflessness and care for the common good, the latter is a scaled up version of the former.

With the rise of social media and software tools to connect people, I find the relation between the two concepts interesting. Let me know what you think.