Sunday, September 29, 2024

Golden Balls: The Ultimate Pareto-Inefficiency

Several years ago, there was a game show that aired in the United Kingdom named "Golden Balls". In the final round of the game, the remaining two contestants choose whether to split or steal a large sum of money. If they both split, then they share the money equally; if one person steals and the other splits, then the person who chose to steal keeps everything. As you may expect, if both parties elect to steal, then they both walk away with nothing. 

I first encountered this game before I had ever studied economics and I was curious as to why everyone did not just split every time - both people walk away happy and they still get a large amount of money. Some time later, after I had encountered the concept of the "Prisoner's Dilemma", I realized that for each individual, it is always better, or at least equivalent, to choose to steal. If the other person steals, then no matter what you do, you get no money (and it may even give you utility to also pick steal to spite the person who tried to take advantage of you). If the other person chooses to split, then it is open season for you to choose steal and walk away with all the money. Of course, if both people think this way, then they will both choose to steal and get nothing, even though they could have both benefited if they both split. And thus we arrive at Golden Balls' Prisoner's Dilemma - both parties would obtain drastically more utility if they both split, but it never makes sense to not choose to steal so two rational individuals would feasibly choose to steal and both walk away empty handed.

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