2011年10月11日火曜日

Golden Balls: Split or Steal

Reading through this article's statistics I saw something very interesting: "Surprisingly, we find little evidence that contestants' propensity to cooperate depends positively on the likelihood that their opponent will cooperate. While an opponent's promise to cooperate is a strong predictor of her actual choice, contestants appear not to be more likely to cooperate if their opponent might be expected to cooperate." Going further, "While a promise is a strong signal of cooperation (according to the statistics those who make a promise are 31% more likely to cooperate), contestants whose opponents made a promise do not have a higher propensity to choose split. In fact, as Model 7 also shows, if an opponent promises to be cooperative, the other player even displays a marginally significant decrease in the likelihood of choosing "split". Though it's hard to say how accurate the results are based on various factors it is nonetheless very interesting and is the basis of my claim.

What I am claiming is that the more certain a player is about their opponent choosing "split" the more likely they would "steal". Or in other words the more uncertain one is about their opponent's decisions the more likely they would "split". Now logically this is quite unclear because it's as though we are saying (in extreme senses) if you know your opponent is going to "split" you are going to "steal" for sure, and if you have absolutely no idea then you would be more likely to "split". But why does this uncertainty play such a role in one's decisions? If you are planning to "steal" if you know your opponent would "split" why should it change your decision if you did not know your opponent would do so? As long as there is even a 1% chance of your opponent to "split" it should still be better for you to "steal".

I asked another friend, who had not studied game theory, in a sort of manipulated way what he would do. I gave him the brief overview of the Golden Balls scenario. I asked him what he would do given that situation and was completely unsure of what the opponent would do. He said he would most likely "share". Then I asked him what would he do if he knew the opponent would "split" he said "steal" because 100% > 50%. Now was this result because he lacked knowledge in game theory? Perhaps. But in a way this decision in a sense is rational. I also gave him the typical situation and he said always "steal" because it always gives you a better result. Either way as for the previous answers I want to compare it a game of matching:

Basically two players (strangers who have not discussed beforehand) have the choice of Left, Middle, Up, Down. If LL, MM, UU they get a utility of (5 , 5). If DD they get a utility of (4 , 4). Any other combination and they both get 0.


Game theory does not really have a solution to this game, perhaps a mixed strategy with less probability assigned to down. In this game the players want to cooperate as their opponent's gain is their own. But without prior discussion and such how can we choose the best method? Going down must be a quite reasonable if not the best choice because out of all the other combinations it is the only unique one (even though utility-wise it is the worst combination out of the three). So in a way in the Golden Balls scenario it feels as though it is possible that people could have used this sort of rationalization because "split" is the only choice that guarantees some sort of plus (even if it is not themselves). The decision of "steal" on the other hand has occurrences where (if both "steal") there would be zero reward to both players. 


Of course if you look at this it's strange because by reasoning in such a way it does not increase the probability your opponent would "split". But no matter how I look at it, it seems as though the fear of your opponent to "steal", in a way almost induces people try to avoid a (steal, steal) situation in which if at the least if they "split" not all of the money deteriorates (even if there is a chance they do not get anything). Perhaps another reasoning behind it could be that in a way by making a move you are hoping your opponent does the same. Again this is sort a dubious idea because logically speaking we do not have some sort of brain control waves in which by making a decision it sends signals to your opponent. But in a way two rational players would look at a chunk of money and by all means would want to avoid the situation of (0%, 0%). The concept to keep the money alive perhaps may influence our decision to choose "split". And this reasoning all comes from the uncertainty of what another player does. In a way you can if you know your opponent would "split" you would "steal" to gain the extra 50% (this is not necessarily true as you may want to share with your opponent or something), and if you know your opponent would "steal" you would "steal" too because if you are going to go down you can at least take him down (this perhaps is inaccurate as you actually might find more "splits" for example because then at least you can look like a good person, but the counter argument of looking like a sucker goes against this too- in the end it's really hard to say but for arguments sake assume "steal" if "steal"). So assuming that your opponent plays in such ways it only seems logical to do "steal" but the uncertainty of your opponent's decision gives one the fear of the potential of playing "steal", And the threat / potential of doing "steal" or "split" has a larger impact than the decision itself or a promise and thus gives a higher likeliness of playing "split" despite the fact that "steal" is rationally the best option. 
So this leads me to the discussion before the two actually make their decision. It puzzled me at first to the reason why they even did this. It should not really matter what your opponent says to you (because you have no ways of making some sort of behind-the-doors agreement) your choice should already be set on in a way, on your values. Thus this leaves me with a conclusion that strategy-wise the best thing to do is during the discussion make it as unclear as possible on what you would do. I mean this does vary among people, for example, if you know that your opponent is a good, trusting person you may instead want to make it seem clear that you would "split", but otherwise in my opinion (and according to the statistics perhaps) by making it so that your opponent has absolutely no idea what you would do, they would play "split".

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