More Prisoner’s Dilemmas

Last week I talked about the Prisoner’s Dilemma, how it can arise in real life, and some of the problems that it presents. This week I want to take a look at it on a larger scale, and use it to map something which might seem more akin to real life. 

First, let’s start with an example of a prisoner’s dilemma. Steve and Terry are five and six years old respectively, and they conspired to get the cookie jar down off the counter and eat all of the cookies. Upon finding the cookie jar, their parents were faced with a problem. One or both of the boys had done it, but they couldn’t prove which one. Sequestering Steve and Terry in separate rooms, each parent offers to cut them a deal. Implicate your brother, and you get off, while your brother gets grounded for twenty-five days. If neither Steve nor Terry talk, then their parents will ground them for two days, but if each of them implicates the other, they’ll both be grounded for ten days. Parenting critiques aside, we can draw up the outcomes in the matrix above. If Terry defects, rolling over on his brother, the worst that can happen is that he’ll be grounded for ten days, while if he cooperates with his brother, it’s possible he could be grounded for twenty-five. The same is true for Steve. If both of them want to be grounded for the least amount of time, then it is rational for them to defect, resulting in a ten day grounding for each.

But it might only be rational if this happens just the one time. After all, Steve and Terry might find themselves in this kind of position a lot. If they both defect in this instance, then they might be more likely to defect the next time their parents pull this stunt on them. Or, realizing how the deal works, they might opt to trust each other more and cooperate. As they grow up, they might go through what we call Iterated Prisoner’s Dilemmas, which changes what’s rational to do in some really interesting ways.

The most interesting thing about iterated dilemmas is that they’re more easily reflected in life. It seems rare to be in a position where you only have to trust someone once and then walk away. Instead, it seems like your relationships are built on a series of these kinds of situations, and knowing that there’s a series changes how you deal with them. If you defect, you have to wonder what will happen the next time. Will they cooperate so readily? Similarly, if someone defects on you, you might see an opportunity to punish them by defecting the next time something comes up.

There are a lot of different strategies for handling iterated prisoner’s dilemmas, and I want to look at a number of them next week. In the meantime though, thanks for reading, and check out this fundraiser I’m helping organize in May. Headshots from the Heart supports Child’s Play, which donates games to children’s hospitals all over the world. We need your support, and so do those kids.