The Prisoners’ Dilemma is a classic problem in economics with a clear theoretical outcome of non-cooperation. In practice, however, people are sometimes “nicer” than economists predict…and apparently this makes the game interesting enough to make a game show about. (Yes, I have been fascinated by this for going on two and a half years now.)
The game show is called Golden Balls (hehe), and the game is called Split or Steal. The setup is pretty simple- there is a pool of money, and each of the two players chooses either split or steal. Furthermore, the two players reveal their strategies at the same time. If both players choose split, then they, not surprisingly, split the pot evenly. If one chooses split and the other chooses steal, the stealer gets the whole pot. If both choose steal, no one gets anything. In other words, this:
This is the classic Prisoners’ Dilemma with one minor twist in that if one player plays steal, it (rationally) doesn’t matter to the other player whether he chooses split or steal, since he gets nothing either way. (This is going to turn out to be quite an interesting feature.) So what would you do in this situation if you could talk to the other player before you choose strategies?
Clearly, your goal is to get the other person to play split, since that is the only way that you are going to get any money. Personally, my initial idea was to convince the other person that I was going to play steal and that he wasn’t going to get anything either way but could come off looking like the good guy if he tried to split.
So why would this work? First off, trying to convince the other person that you’re going to split should be a non starter, for two reasons. First, the steal strategy (weakly) dominates the split strategy- if you think the other player is going to split, it’s clearly better to steal, and if you think the other player is going to steal, stealing is just as good as splitting. This means that convincing the other person that you are going to split is an uphill battle because the other person can see that splitting isn’t in your best interest. Second, even if you can convince the other player to split, all that does is give the other player a greater incentive to steal.
Given this, the only reasonable options are to either not promise anything or to convince the other person that you are going to steal. It shouldn’t be hard to convince the other person that you are going to steal, since stealing is in your best interest. (I would probably explain to the other guy why stealing was in my best interest in order to build credibility.) If he is convinced that you are going to steal, the other person should be (rationally) indifferent between splitting and stealing, since he doesn’t get any money either way. (Yes, I get that there might be a psychological incentive to punish, but that isn’t “rational” from an economic perspective.) Therefore, all you should have to do is provide some incentive to tip the scale towards split for the other guy. What’s interesting is that the other person doesn’t have to fully trust you for it to work, they just have to believe that there is some positive probably the the incentive will come to fruition.
So what actually happened?
As an economist, I don’t think this is weird at all, and I am both shocked and not shocked that this doesn’t happen more often. Perhaps somebody should hire this guy into an economics department.