Golden Balls: Splitting, Stealing, and Mastering Manipulation
https://www.youtube.com/watch?v=p3Uos2fzIJ0
https://www.youtube.com/watch?v=S0qjK3TWZE8
During freshman year, a few of my friends took PSYCH 1101 and learned about a British game show called Golden Balls. I watched a few episodes with them and was instantly fascinated with the show. Golden Balls has two rounds where a pair of people work together to accumulate a pot of money. Then, they reach the final round called Split or Steal, which is a pseudo Prisoner’s Dilemma problem. Each player decides whether they want to split the money, or steal from the other. If they both split, they split the money and each get half. If they both steal, they walk away with nothing. If one splits and the other steals, the stealer keeps the whole sum. The expected payoffs can be summarized in the table below.
| Player 2 | |||
| Player 1 | Split | Steal | |
| Split | (.5, .5) | (0, 1) | |
| Steal | (1, 0) | (0, 0) | |
In the Prisoner’s Dilemma, if one player chooses to defects, the other is better off defecting as well. However, in Golden Balls, if one player defects (steals), then there is no good strategy for the other player as they will be left with no winnings no matter what. Thus, there are three Nash equilibria in Golden Balls, which are the three scenarios in which a player decides to steal.
The two clips I attached offer two differing perspectives to the show, but these clips were what made me fall in love with Golden Balls. The first clip details a classic Split or Steal situation where Sarah deceives Steve and takes everything (over 100,000 pounds) from him. The utter despair Steve faces and the cruel composure Sarah displayed roped me in and I couldn’t stop watching clips of this show. Then, my friends and I found the second clip. Without any formal knowledge of game theory, I thought this interaction between Nick and Ibrahim was absolutely brilliant.
One of the things that makes the Split or Steal segment so much more heart wrenching is that they allow the contestants to talk about their strategy for about 30 seconds before they choose whether to split or steal. Thus, you can witness someone like Sarah coldly lie about their strategy. However, in the second clip, Nick makes a move that at first seems so incredibly scummy. He comes right out and tells Ibrahim that I’m going to steal, but I will split the winnings with you after the show. The pair continued to go back and forth and as I watched, I grew increasingly frustrated with Nick for opening and controlling the conversation. As a result of this conversation, the outcome that Nick is promoting (and seemingly the only two options) is now highlighted in blue.
| Ibrahim | |||
| Nick | Split | Steal | |
| Split | (.5, .5) | (0, 1) | |
| Steal | (1, 0) -> (.5, .5) | (0, 0) – > (0,0) | |
If Ibrahim chooses to believe Nick, which he has no reason not to since Nick has been adamant that he will steal, Ibrahim is effectively trapped into splitting. This feels like a paradox almost because Ibrahim will be agreeing to letting someone else take all the money, with no surefire guarantee that any will come his way. If he trusts that this money will come back to him after the show, however, the probabilities have shifted for the Split and Steal outcome where now instead of receiving none of the money, Ibrahim would get ½. If he steals, he still gets none, so Ibrahim will decide to steal, and hope that Nick honors his word.
When they reveal their golden balls, Ibrahim has, in fact, split. Nick, however, shockingly decided to split as well. After telling Ibrahim all along that he was going to steal, he split. Without any knowledge of game theory, I remarked to my friends that Nick was absolutely brilliant as he found a way to seemingly guarantee that they would both split. He forced Ibrahim not to steal by stating that Nick was going to steal no matter what. Now, looking at the decisions and using the knowledge from class, Nick had effectively shrunk the board into two options. Within these options, there was a mutually beneficial strategy, so they both participated. By shrinking the board, Nick made splitting a dominant strategy for Ibrahim because it was the best response to every strategy Since Nick was able to guarantee that Ibrahim would split, Nick knew that he could split and they would leave with half of their pot.
Golden Balls serves as another real-life example of game theory, similar to the Prisoner’s Dilemma, but the contestants were allowed to talk, so they have an opportunity to attempt to form a decision through contact with each other. This usually ends problematically and both players steal, but Nick controlled the conversation and set the duo up for mutual success. My intuition to Nick’s brilliance is confirmed by game theory, he shrunk the board and was able to seemingly manipulate the rules of the game by exploiting a flaw, and as someone on YouTube commented Nick is a “very clever man” and “probably why the show ended.”