The Golden Balls is a pretty standard UK game show. It has a traditional set, a brightly lit stage, large props, and a vicious, competitive game played for large amounts of money. The game is set up based on the Prisoner's Dilemma. Two contestants each are presented with two golden balls. Inside one ball, the word "steal" is written. Inside the other, "split." The two contestants each choose a ball and reveal it at the same time. If both contestants "share," they split 100,000 pounds. If one chooses "steal" and the other chooses "split," the stealer walks away with all of the money and a guilty conscience. If both people choose "steal," they both lose it all.
Here's the catch though. Unlike in the traditional Prisoner's Dilemma, the contestants are allowed to talk with each other before their choice. In fact, they are given an indefinite amount of time. They can argue and plead with each other for as long as they want until they both agree to make the final decision. Usually, this just results in the two people promising over and over to share, though there are countless examples of shameless backstabs and betrayals by people who would otherwise be upstanding. This is because operating from the assumption that the other person could choose either option, you stand a better chance of making money if you choose steal.
Obviously, this is a vicious game, with no really secure choice. However, one time, a contestant named Nick decided to upend the entire system. Instead of pleading and pleading for a mutual "share" agreement, Nick led the conversation from the very start, with a new strategy. This is what he told the other contestant as soon as the deliberation period began: "I want you to trust me. 100 percent I am going to pick the steal ball. I want you to choose split, and I promise you that I will split the money with you." This decision completely rearranges the profit opportunities for the other contestant. If he operates off of the base assumption that his opponent automatically chooses to steal, he has no chance of stealing himself. But if he chooses to share and let Nick steal from him, he has a certain chance of making money, on the hope that Nick is honest and will truly just hand him the money after the show ends.
This argument lasted for an hour, where Nick stood steadfastly certain at his steal choice, and the other contestant, flustered, could not find a better way to operate, so he gave up. They agreed to make the final decision. The big reveal came. As expected, the second competitor had chosen "share". But when Nick revealed his ball, it also read "share." Both contestants walked away with half of the money, one happy and content with himself, and the other still confused and a little bit angry, but with a wallet 50,000£ heavier.
Sources:
https://mindyourdecisions.com/blog/2012/04/24/how-to-beat-the-prisoners-dilemma-in-the-tv-game-show-golden-balls/
https://blogs.cornell.edu/info2040/2012/09/21/split-or-steal-an-analysis-using-game-theory/
This is a really interesting application of game theory, especially with the story about the contestant mentioned, Nick. He must have realized that if he convinced the other person to both pick share/split, there would be a good chance that the other would actually choose steal, and leave with all the money, because based on game theory that would be the best decision for that other person. However, if he convinced them he would choose steal, if the other person chose steal then neither of them would get any money, so the opponent had no choice but to choose share/split. That way, Nick could choose split, and they would get to split the money, rather than risk getting no money.
ReplyDeleteI really like this application of game theory. I enjoyed reading about this specific example. I was also really fascinated by the specific example you mentioned, and the strategy that Nick decided to choose. It makes sense that he would do this, and it's very smart for him to find a way that almost guaranteed he would get money by having the other player select split. If he was coming in with the notion that he wanted to make money, but didn't want to make the maximum amount, this was a great strategy. There is a way larger risk if one person is willing to steal the money, and not agree to share it, so with Nick's goal to just win money, this was a very smart decision. With Youtube today, I've seen similar games on the channel Jubilee where they use the same concept but with groups. They also are able to discuss beforehand and explain their backgrounds. It's always interesting to see what the teams choose. In the comments it's often overflowed with people saying that it would be best to steal, but that risk may not be worth it when there are ways to almost ensure that your opponent will select split.
ReplyDeleteThis strategy can only work once because once both contestants know that the first person will choose share, then the second contestant's options have changed. Instead of choosing between winning nothing and having a chance of winning half, he can chose to steal and possibly win everything. This reverts back to the classical Prisoner's Dilemma where each contestant is unsure of the other's actions, as the first person could be bluffing about the strategy to say steal then share, and instead chose to steal.
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