Can irrationality trump rationality?
Offline I hope this is the right forum. Logic and psychology seem to fit.
I recently read an article in a Scientific American magazine. Conveniently it is online should you also wish to read it. It explores how games theory predicts the rational responses within limited choices for the best result. Here is a quote I found interesting, and will hopefully interest you enough to read the article.
<quote>Forget game-theoretic logic. ...both of us will ignore the rational argument ... What is interesting is that this rejection of formal rationality and logic has a kind of meta-rationality attached to it. If both players follow this meta-rational course, both will do well. The idea of behavior generated by rationally rejecting rational behavior is a hard one to formalize. But in it lies the step that will have to be taken in the future to solve the paradoxes of rationality that plague game theory ....
-Kaushik Basu </quote>
I am curious to know other peoples opinion on this.
My take is that games theory is resting on the false assumption that behaving rationally will garner the best results.
Can rejection of rational behavior itself be rational? After rejecting rational behavior how do you form your decisions? As stated, this seems paradoxical. If either you or your opponent choose an irrational choice, games theory will fail in its predictions. Thinking about this makes my head go around in circles, but it seems like if you remove that assumption from games theory (because you believe it to be false) then you can strategize rationally for a superior strategy than games theory with that assumption can predict. I don't even really understand my own thoughts on this, I am hoping you can help shed some light in this corner of my thoughts.
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The "behaving rationally" part is most likely the economic influence on the wording. As pure math, game theory only illustrates possible outcomes from players' behaviour. "Behaving rationally" is redefined for someone who has an understanding of those outcomes, as opposed to someone operating on intuition. But "rational" in the economic sense is the attempt to act in one's best interest. It's not necessarily "logical" or "mathematical" thinking.
However, it would be rational behaviour in both senses to play for a Nash equilibrium where one existed.
Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum. - Terence
The article I linked cited a study where the participants were limited to a particular association of games theorists with a real life monetary reward. The majority of them rejected playing the nash equilibrium, and the strategy that got the best results was not the nash equilibrium games theory predicts. Acting in thier best interest turned out to be rejecting the nash equilibrium. This seems to allow for rational decisions to reject games theory if you can predict with a degree of confidence that your oppenent will as well, for whatever reason. Specifically it suggests there may be a rational reason for rejecting the nash equilibrium apart from intuition or failure to logically reason out the consequences of the decisions made. The article mentions reciprical altruism to dismiss it, but I am not so sure it should. The paradox intrigues me, that it can be rational to behave irrationally.
Feigning irrationally can be used as a rational tactic.
An example:
http://www.wired.com/politics/security/magazine/16-03/ff_nuclearwar
People who think there is something they refer to as god don't ask enough questions.
I think I found a flaw.
I have little background in this field, so I would not be surprised to find I am wrong. Please let me know if I am and point me to where I can educate myself.
Nash equilibriums seem to apply to people who play the game with the goal that can be stated "best payoff I can get." The goal "a better payoff than anyone else" especially when you include players you are competing with only indirectly will rationally result in a different strategy.
The author is incorrectly equating those two goals, and introducing the additional factor of indirect competition. There is no nash equilibrium in such a game. If this is true, any conclusions that require its opposite are invalid.
Edit - Not changing anything above, even though it does indeed display my ignorance. The payoff wasn't to the player that was better than everyone else, it was to a random participant based on thier average payoff. That seems to me to motivate the player to seek selfishness vs superiority. If superiority isn't required, indirect competition isn't a factor. I did not find a flaw after all, and I am still bewildered.
That was an interesting read aiia.
Russia had more reason to fear annihilation than we did during the missle crisis. I never read about that in any history book.
Nevertheless, their posturing was a reasoned act calculated to exact a specific response. There was risk that thier calculations were off, and the penalty for being wrong would have been irreparable. I can't say whether I think they made the right choice, but they still made thier choices believing them to be reasoned out, rational and sane.
I think there might be some connection, perhaps weighing the results of how your oppenent would behave if he expected you to behave irrationally, that has some bearing on why discarding the seemingly rational choice could give better results.
With a reward disproportionate to the penalty, the incentive to promote irrationality (for yourself and your opponent) increases. Even knowing this, you can have the expectation that rational beings know when to rationally behave irrationally without any feedback loop. I guess my main confusion is once you decide that behaving rationally is out, how can you come to a strategy that you will have any confidence will be better than any other? Its one thing to rationally feign irrationallity, but to rationally decide to behave irrationally and come out ahead? My brain is exploding.
It's still Tit-for-Tat (optimal group strategy for prisoner's dilemma), and the reason why I argue that we should all act for mutual benefit.
After reading the article, it appears to me that the author somehow ignores the fact that he's not dealing with a single-step game. There's also an implied coalition, which doesn't end up making sense. The resulting survey experiments discount the decision heuristic that exists outside of a payoff matrix, which is frankly childish.
Actually, to start at the beginning, the Nash equilibrium concept is pure math. By that, I mean that it really appeals to economists because they like feeling legitimate. People apply all sorts of heuristics in any environment more complicated than a payoff matrix, because to do otherwise would be irrational. The people in the experiments are not acting irrationally, for instance, if they choose the maximum (rather than max - 1) since, by an external heuristic, that will benefit them a certain fuzzy amount. Choosing the maximum amount, and assuming others would do the same, presents a coalition situation, which is addressed elsewhere.
I guess the author is trying to meet the Nash problem on its own turf, but it's really unnecessary. Economic use of the word "rational" has always been a problem.
Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum. - Terence
... assuming we can figure out what that is. In the case of the prisoner's dilemma, it's a 2-by-2 payoff matrix. With actual life, the variables are almost unlimited, so it becomes more practical to use a simplified heuristic based on a fuzzy probability. If you can introduce coalition, then certainly mutual benefit can exist. But economists concern themselves largely with market environments, where individuals find themselves somewhere between competition and cooperation.
Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum. - Terence
It's not a case for irrationality.
It just points out that people who build a relationship and work together will do better than those who just try to get the better of their 'friend' instead.
So it becomes rational to build up a relationship that encourages cooperation, and while this will result in the odd loss, you win overall in the long run.
Much better than the minimal gain you'd get for starting a war and losing a lot in the long run.
So it's rational to build relationships than compete for short term gains.
As others have said, the solution to the prisoner's dilemma is indefinite playing of the game. Society is a lot of individuals playing slightly modified Tit-for-Tat strategies (IIRC, the optimum is being slightly forgiving... avoiding mutual defection loops by returning to cooperation after the first, and sometimes a few more, defections) with LOTS of people at the same time.
When scientists first started looking at the prisoner's dilemma, they noticed that most of the people who played, say, 100 rounds weren't playing it 'logically.' Their explanation was that the people weren't sophisticated enough to figure out the logical way to do it. It turns out, the scientists weren't sophisticated enough to know that the people intuitively figured out the most logical thing to do. As long as there was no foreseeable end to the game, mutual cooperation was the correct, and most logical, way to play. Towards the end of the game, defection was more profitable, since there would be no sanctions later.
Human society is an endless game. Though one person dies, he is part of a society, which is essentially an endlessly overlapping series of games. What mathematicians forgot when they first started working with game theory was that in sentient beings, reputation matters.
Atheism isn't a lot like religion at all. Unless by "religion" you mean "not religion". --Ciarin
http://hambydammit.wordpress.com/
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Exactly. It's also extremely difficult to model human behaviour as a 2X2 matrix. Surprise, surprise. Humans aren't really equipped to deal with such a one-dimensional environment anyway, so it would be (again) no surprise that we would solve the problem with a sizeable degree of error.
Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum. - Terence
I'd hazard the guess that when mathematicians work on game theory, they're well aware of the problems presented by a system "with memory". It's when philisophical economists and popular culture start jumping to unreasonable conclusions and form expectations based on the math that the modelling gets unreasonable.
Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum. - Terence
I was only speaking of the first who looked at it. Mathematicians figured it out pretty quickly.
Atheism isn't a lot like religion at all. Unless by "religion" you mean "not religion". --Ciarin
http://hambydammit.wordpress.com/
Books about atheism
I think I just have a deep and abiding need to pick on economists, and it's on a hair trigger. Misfire.
Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum. - Terence
Hair trigger or no, I think it's probably a well founded desire. Definitely this kind of idea is misused and abused when the public gets a hold of it.
Atheism isn't a lot like religion at all. Unless by "religion" you mean "not religion". --Ciarin
http://hambydammit.wordpress.com/
Books about atheism
Isn't this generally called "Rational Egoism" in Game Theory, to distinguish it from the Enlightenment/modern-era concept of rationality?
“It is true that in the land of the blind, the one-eyed man is king. It is equally true that in the land of the blind, the two-eyed man is an enemy of the state, the people, and domestic tranquility… and necessarily so. Someone has to rearrange the furniture.”