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Prisoner’s Dilemma in Golden Balls Game Show

For those not in the know, Golden Balls was a short-lived British game show that ended airing about a decade ago. In the show, four contestants compete for a cash prize. For our discussion of Prisoner’s Dilemma, we will look just at the last round of the show. In the last round, the remaining two contestants converse and decide what to do with the prize, split the winnings 50/50 between the two of them or steal the pot for themselves.

If both decide to split the total, they both will get half. If one splits and one steals, the one who stole takes all the winnings. If both opt to steal, they both end up with nothing. In short, this scenario is a take on Prisoner’s Dilemma.

 

Split Steal
Split 50%, 50% 100%, 0%
Steal 100%, 0% 0%, 0%

 

Often, contestants will offer to split, as this is the mutually beneficial option. However, this is a sub-optimal strategy. Take a look at the payoff matrix, given you know the other contestant will split.

 

Split
Split 50%, 50%
Steal 100%, 0%

 

It is clearly visible that now there is a best response option for the other player, given their goal is to maximize their own payoff. The contestant who is being offered a split very often realizes this, and opts to steal.

In one taping the last two contestants, Ibrahim and Nick, reach the final round and must decide to split or steal. However, Nick takes an unorthodox route, stating that no matter what Ibrahim does, Nick himself will choose to steal. Nick tries to convince Ibrahim to choose split, and then Nick promises to give him half of the winnings after the show; although this would not be a binding agreement. This leaves Ibrahim in a unique predicament.

 

Steal
Split 0%, 100%
Steal 0%, 0%

 

Assuming Nick will steal, Ibrahim really has no chance to take the winnings. All he has is Nick’s word that he will split with him after. If he splits, Ibrahim is betting on Nick keeping his word. If he steals, he may deny Nick but he himself has no chance at any payoff. Ignoring emotions and assuming each player is merely looking to maximize their own payoff, Ibrahim should choose split as this is his best response given the circumstance. Ibrahim does opt to split, but Nick flips the script on him and also chooses to split.

By declaring his intention to steal, Nick guaranteed himself a payout, as Ibrahim had no real choice but to choose split in order to have a chance of payoff. In this fashion, Nick managed to “break” the dilemma of the game show by forcing his fellow contestant into splitting. If Nick were really cruel, he could have even actually chosen to steal and take home all the winnings!

Looking at the Golden Balls game show, we are given a real-world example of Prisoner’s Dilemma. Observing the show, one can quickly realize that often people allow their emotions to dictate their decisions, as contestants often generously offer to split, thus allowing themselves to get burned. Golden Balls gives insight into how game theory is merely a basic template model for people’s decision making, but often times players allow external factors to influence them, rather than just focusing on maximizing their payoff.

 

Link: https://blogs.pugetsound.edu/econ/2017/11/09/heart-of-gold-game-theory-in-game-show-golden-balls/

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