Game Show “Golden Balls” epitomizes Game Theory
I came across this very interesting game show called “Golden Balls.” This game is similar to many American game shows — it involves competing individuals who are ultimately trying to get as much money out of the game as they can. Golden balls involves two players who progressively build up a jackpot of money, and in the last stage of the game they get to choose whether to split the money or try be greedy and to take all of it. This last element of the game is the epitome of Game Theory. Each player has two balls — one contains the word “Steal” and the other contains the word “Split.” Depending on which ball each of them chooses, there are three potential results:
1. if both players pick “Split” then they split the jackpot evenly between the two of them,
2. if one player picks “Split” but the other chooses “Steal” then the player who chooses “Steal” walks away with all of the money, and
3. if both players pick “Steal” then neither of them receives any money.
Here are links to two short videos showing episodes of “Golden Balls.” They have different outcomes and in each episode the players have different strategies and take different approaches. I find that this episode is more stereotypical and predictable, while this episode is very intriguing and somewhat surprising. These videos (along with several others) ultimately show that humans are generally greedy. A select few episodes made me appreciate humankind, but most brought out feelings of extended remorse and disgust for some of these individuals playing the game.
“Golden Balls” incorporates a variation of traditional Game Theory, where the decisions of one person depends on the impending decisions of another. However, the players are allowed to talk to each other and thus more factors are involved in the decision making of the participants. This game would be slightly more straight forward and the outcomes would follow more of a predicable pattern if the players couldn’t converse with each other (like in the example of the “Prisoner’s Dilemma”), but they CAN. Separate from their own degree of morality and greediness, each player has to not only take into consideration the trustworthiness of their opponent, but also they must analyze their body language and verbal proposals.
Let’s give a scenario with player A, player B, and £50,000 on the line. To reiterate, two splits result in sharing the money, one split and one steal results in the stealer receiving all the money, and two steals result in no money for either player. If player A initially comes out very passive, reserved, and content with splitting the money, player B can think a multitude of things. First, let’s assume that player A is completely honest and their body language and suggestions for splitting match their actual intentions. Player B, depending on how kind or greedy they are, could mirror the same attitude of cooperation and sharing as Player A. Both would pick “Split” and walk away very happy with £25,000. However, people aren’t that simple or nice, so this outcome is very unlikely, and very lucky. Instead, Player B could take advantage of player A’s kindness and choose “Steal,” taking all of the money. On the other hand, let’s assume player A outwardly expresses cooperation and wants to split the money, but in reality aims to sway player B so that they choose “Split” and player A then chooses “Steal.” Many episodes have players who follow this approach, and it’s somewhat devastating to see genuinely nice people get stabbed in the back by selfish, manipulative people.
Sometimes both player A and player B take the approach of pretending to want to choose “Split” but in reality choose “Steal,” which results in both of them receiving no money. This outcome most accurately resembles true game theory and the prisoner’s dilemma. Without accounting for body language or verbal communication and just isolating the decisions to choose “Split” or “Steal,” the double “Steal” result should happen most often. If you calculate the benefits of the various options for player A and B, the Best Response for both is to choose “Steal,” and thus nobody receives any money. In a greedy world, if player B chooses “Split,” then player A should choose “Steal” to get £50,000. If player B chooses “Steal,” then no matter what player A chooses, player A will receive £0. Thus, player A should choose “Steal.” The same goes for player B’s decision in the opposite direction. If player A chooses “Split,” then player B should choose “Steal” to receive the biggest benefit (£50,000). And if player A chooses “Steal” (which, from before, they are going to do), the it doesn’t matter which option player B chooses because they will get no money either way. Thus, player B should pick “Steal.” Therefore, this last round game is setup so that both players should normally choose “Steal,” will receive no money, and the show loses no money, because the “Steal” option for both is Nash Equilibrium.
In the second episode that I gave a link to, one man takes a very interesting approach to the whole situation. Normally, since the players are allowed to converse and “strategize,” they really can never know what the other person is going to do. Each person’s choice is still very ambiguous, and the players are normally left to trust the other person. However, in this episode, one man clears away all ambiguity by saying “100% I am going to choose the steal ball, and then afterwards I will split the money with you.” As I discussed above, given that he will take the “Steal” ball, it doesn’t matter at all (in terms of personal benefit) to the other man whether he chooses “Split” or “Steal.” The fact that the first man claimed that, with certainty, he was going to choose the “Steal” ball took his ambiguous decision out of the equation, and left it up to the other man to choose the fate of the game. The first man was able to pretty much confirm that the other man was going to pick “Split,” and by doing so the first man could comfortably pick “Split” himself to actually split the jackpot amongst the two of them.
It’s impressive how this game show really embodies the philosophy of game theory in such a realistic way. I also find it absurdly disgusting how some people are so greedy when it comes to money and how manipulative they can be by pretending to feel one way but act another way. I hope you find these videos intriguing and the logic behind their decision making fascinating as well!
Sources:
Clip 1: https://www.youtube.com/watch?v=yM38mRHY150
Clip 2: https://www.youtube.com/watch?v=S0qjK3TWZE8