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RE: Mathematically, people are selfish
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?
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.
Very interesting. Thanks for giving an example of how you could generalize ;)