Prisoner’s Dilemma, Russell Crow and Some Stupid Golden Balls

Watch this video first.. then proceed…

This game is very interesting because watching it and understanding the decisions made in the game can actually simplify some extremely complex, Nobel-prize winning economic science. Let me begin with I am not even close to an expert in these ideas and concepts.. but here goes..

Let me repeat the rules. The game show in the video is called Golden Balls. Two players have to decide to pick either a ball with split of steal. If they both pick split they split the money. If they both pick steal they get nothing. Where it gets interesting is if one picks steal and the other picks split then the “stealer” gets it all and the “splitter” gets nothing. This is something that is described in Game Theory as the Prisoner’s Dilemma, where basically two crooks are forced to confess independently and given similar incentives they are offered to a) rat out the other crook and one possibly go free, B) confess and possibly both split the time or c) stay silent and possibly both get the max sentence. John Forbes Nash, some of you might know portrayed by Russell Crown in the Beautiful Mind movie, was a mathematician and game theorist who came up with something called the Nash Equilibrium. Nash Equilibrium has been used in war games, arms race models as well as the famous 1994 FCC airwaves spectrum auction. You probably remember the FCC auction as the time you had to throw away all those rabbit ear antennas after you were told they would not work any longer.

In the movie, Beautiful Mind, the Nash Equilibrium theory is grossly explained by four young men trying to figure out how to pick up girls (you gotta love Hollywood). I will spare you the details of the theory because it typically makes my head hurt when I try to explain it. So to keep it simple here’s how it can be explained using the Golden Balls game show. Basically the game show Golden Balls is an example of a Nash Equilibrium if you look at it from an incentives and strategy perspective. Looking at each player by identifying their strategies as dominate and equilibrium’s (choices where the players incentives are balanced) you can see the structure of a Nash Equilibrium. In this case, one of the players, Nick, clearly understood game theory and most likely understood Nash Equilibrium. Ironically Ibrahim kept calling him crazy (crazy like a fox eh).

The Golden Ball game basically has a polarity towards contestant’s incentives always stealing. That’s what makes the show interesting. In fact, it has been reported that very rarely did contestants on the show both pick split and actually split the money. If you are so inclined, you can watch some videos on game theory and Nash Equilibrium to understand the combination of choices that are dominant strategies and are also considered Nash Equilibriums. Alternatively, I can tell you that the dominant strategies and Nash Equilibrium’s in this game are steal, always pulling contestants towards steal even though most contestants don’t even know game theory. Just like the crooks in the Prisoner’s Dilemma who are actually be “gamed” by the cops.

Here’s where it gets really cool and why the title of the video is called “the weirdest split or steal ever”. What Nick did is convince Ibrahim that he was going to choice steal no matter what. He also gave a little nudge of motivation with his offer to split the money after the show. What Nick did is masterfully change the game’s polarity (incentives matrix). Instead of the game being pulled (incentivized towards steal) he changed the incentives to split. In this case, he was able to force Ibrahim’s incentives and dominant strategy to split instead of steal (even though Ibrahim didn’t realize he was being “gamed”). This gave Nick a more likely chance of winning instead of losing. In other words, once Nick convinced Ibrahim he was going to steal he removed all of the payoff incentives for Ibrahim to steal. In fact, the rules of the game were actually changed after this show

to make this less likely to happen in future episodes. The irony here is that I believe most people actually want to split, in the Golden Ball game and in life, but typically don’t get the opportunity due to the scenarios which purposely positions the human factors of trust and greed against each other. Of course, that’s what makes the show exciting and of course sometimes life.

Still confused? Here’s another link to a presentation where I go into more details about the game and how it relates to a Nash Equilibrium: