Golden Balls Introduction

This post is just a general introduction to my next post and thus not necessary to read (if anyone is reading anyways). The idea behind this post also came from a friend who was contemplating on discussing game theory for his paper and these are mine / our conclusions to the situation. Of course his paper is focused on a completely different aspect.

I have somewhat recently came across a clip on Youtube which displayed a very interesting example of the prisoner's dilemma. The basic summary of this is there are two players who are faced with a decision to split or steal a certain amount of cash (average of $20,000 source). If they both split they get 50% each, if one steals and the other splits the one who steals get's all the money while the other gets none. In the situation that they both steal they both get nothing, unlike in the "typical" model where there is some sort of consolation prize.

 

 (From now on I would be referring to the model on the right as the typical model)

The difference in this case is that instead of having strictly dominating strategies we only see weakly dominated strategies as each player is indifferent between stealing and splitting when their opponent steals. 

In the theoretical standpoint we would see the same results between the two, where both players steal and end up getting nothing or 10%. In both cases there is an obvious Pareto improvement (where at least one player can benefit without harming the other), which is (split, split) gaining 50% as opposed to 0% or 50%. But in the Golden Balls situation we see that (steal, split) or (split, steal) is a Pareto improvement too. For both situation we see that by playing through game theory the result is an unfavorable one.

Now looking at it in a psychological perspective is quite interesting. In both models compare the choices one player can make considering that the other player would split. With this viewpoint we are comparing 100% if steal with 50% if split. Game theory tells us 100% > 50% that's your decision. But the reasoning behind this can really only be said to be as greed. Whether there is a negative connotation behind that or not cannot really be said as it is almost as if asking someone would you rather have $100,000 or $50,000 (if you do not consider your opponent). To me more interesting though is the decision made assuming your opponent steals. In the Golden Balls model we see that a player should be indifferent between stealing and splitting as they would get nothing no matter what they do. But in the typical model stealing would allow you to have 10% rather than nothing at all. In this sense it, stealing almost acts as a defense mechanism. In this post (link), I discuss extreme situations of the prisoner's dilemma where such a defense has a much larger impact. So in a way, the decision maker in Golden Balls is really only looking at whether to split or steal based on their opponent splitting. In that perspective we see that you are looking at two categories of people (ie. the benevolent sharing kind, and the greedy). Of course there are various other factors which I would discuss later. In the case of the typical model though I would say that being unsure of your opponent stealing is a likely reaction (without considering the extra money you get if they split) because it defends you in the case that your opponent steals. With that in mind, there should be a large number of the "benevolent" people using steal thus if tested we should see a higher % of steals in the typical situation compared to golden balls.

Out of the 574 final contestants, 53% of them chose to split. (link source) To me this is a very surprising number in that it is really quite high. There are quite a few somewhat obvious reasoning that can be drawn. Just as one would gain some sort of sense of well-being when offering their seat to the elderly, the decision for a player to do split can add the gains to themselves based on making their opponent happy. Of course in such a situation it probably only has that effect when the other player splits too, as I would definitely have some sense of added disutility given I trusted my opponent yet he backstabbed me. Another idea is that being on television you do not want to be seen as an asshole by stealing. The article mentions there is a counter effect in which you also do not want to be seen as a "sucker" by splitting. But to add to that I also feel as though given the situation of the cash prize, having your amount of money doubled should not really play too much on your image. In a way you can almost say it gives you a positive image in the sense that you outsmarted your opponent (of course this is dubious, you may also be seen as a psychopath). There is also probably the group of people who can be said to be genuinely good and would share no matter the situation as even if their opponent steals the result is nothing anyways.

But the reason I started this blog, was because it seems as though the most curious aspect of uncertainty may be the one that has the largest impact on the decision to split. While this is unclear and perhaps counter logical (because it shouldn't matter whether you know what your opponent would do as you really are only considering what they would do if split) yet in a way can be rational. I discuss this idea in this blog post (link).