We had a very interesting lecture today, which turned out to be quite disturbing.
The topic in question is game theory.
Game Theory's official definition is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers" (Roger Myerson, Game Theory: Analysis of Conflict, Harvard University Press, 1991). This basically is a mathematical prediction of how people (or companies) will act when they have to deal with other people concerning choices which influence or can be made by all the parties involved.
The film Beautiful Mind is about John Nash who was a major player in the development of the theory.
One of of the examples the professor used was the Centipede Game. The Centipede game's rules are very simple. Two players, say Jack and Jill are sitting at a table. $10 is placed on a table. Jack can choose first, and he can decide whether he wants to take the money, or pass. If he passes, another $10 is placed on the table, making the pot $20, and then it is Jill's turn to decide. This continues until some upper bound, say $70. If they reach the $70, the pot will be split evenly, so each player gets $35.
Instinctively, one would say it is the best strategy for both players to go until the end so that both players get $35. But according to the mathematical view of human nature this won't happen. Mathematics assume that people will always do what is best for themselves. So, when the pot is $60, Jill has a choice. She can choose either to take the $60, or passing which means she will only get $35. So mathematically, we can assume that she will take the $60. But Jack knows this and therefore he will rather take the pot at $50. But, once again, Jill knows this, so she will take the pot at $40. This continues back until the start where the best mathematical choice for Jack is to just take the $10. Bizarre. Both players can walk away with $35, but the best strategy for Jack is to take $10.
Luckily, Game Theory is slightly more complex than this. The centipede game is only an example where you assume that the parties have no love for the opponents. Empirical results show that most games actually continue to the end, so there is still hope for humanity! To use game theory in real life a lot of simplifying assumptions need to be made.
In the article http://levine.sscnet.ucla.edu/general/whatis.htm they use game theory to prove that the statement "If we were all better people the world would be a better place" is false.
Mathematically, game theory makes sense. Humanely, intuitively, it is completely absurd.
Every choice companies make is based on millions of calculations to find the optimal strategy. My concern is that they lose their humanity in all those numbers.
Great Post! Do you know of any modifications that people have tried to make to game theory in order to make it work for games like this?...for instance does anyone study "intelligent rational decision makers" where "rational" doesn't exclusively personal profit seeking?
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Thank you! Game theory actually uses the word utility instead of profit. Utility can suggest profit made, or it can suggest greater fame or any other thing which can be gained or lost by playing "the game". But it always needs to be quantified. So in the centipede game example, if you want to create a scenario which is closer to real life, you will have to add an utility of say, honour, meaning you will lose honour if you take the money without sharing with your opponent. If the honour utility is quantified as $60, then the players will play until the end because their total utility gain would be negative if they take the pot (say $10 - $60 = -$50). If the honour utility is quantified as $30 then the player will take the pot as soon as it reaches $40 which will result in a net gain of $10. So the question is, how would one quantify moral values? And once quantified, it suggests that there is always a value above the quantified value. So a company would not break the law if someone paid $100, but would they do it if they are paid $100 000 000 000? Probably.
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Very interesting. Thanks for giving an example of how you could generalize ;)
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Interesting read! If you do not mind me asking, what is your area of study at University? And what class did you have this lecture in?
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Thank you! I am a final year actuarial student. This was in an actuarial module, Statistical Methods.
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Hi, I'd like to include a link to this article in the next math-trail magazine. I hope that's fine with you.
!-=o0o=-!
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Thank you very much! I would be honoured
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