Golden Balls: The Strategic Act of Betrayal (Game Theory)
Golden Balls is a British game show that brings out the deceitfulness within its contestants. Up until the final around, players build up a jackpot that, in the end, two finalists compete for. In this final round, the jackpot can either be taken by one person or split between the two; the outcome is decided by game theory:
Each player is given two balls, one that says “steal” and one that says “split. If both players choose split, then they each take half of the jackpot home with them. In the event that one chooses split and the other chooses steal, the one who chooses steal will take everything. Finally, if both choose steal, both walk away with absolutely nothing. (Below is a table to visualize this information (first number is player 1’s pay off, second is player 2’s))
In one of the most iconic final rounds, a man named Stephen and a woman named Sarah have a short discussion before choosing a ball. There is already quite a lot of tension as Stephen has already crossed Sarah in a previous round. However, Stephen makes a quite convincing plead, telling Sarah “if I stole off of you, every single person there (audience) would run off and lynch me” and “I can look you straight in the eye and tell you I am going to split”. No matter how genuine he was, he was rather foolish to believe Sarah’s empty promises as in a (not really) surprising turn of events, Sarah chose steal when he chose split. Of course, she got a lot of negative reactions; while a rather deceptive, cold decision, she was purely playing the game.
In this game, it is a dominant strategy to steal since in this game, the two people are strangers and care about their own self interests. If player 2 steals, player 1 will have a pay off of 0, regardless of his/her decision. If player 2 splits, player 1 has a better pay off with steal as 1 > 0.5 (this pay-off analysis works the other way around as well). While split/split seems like the moral, ideal outcome, Sarah couldn’t trust Stephen and decided to be strategic rather than sympathetic.
source: https://www.joe.co.uk/entertainment/recalling-the-most-savage-act-of-treachery-in-the-history-of-television-84835