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Bayesian Decision Theory - --Pete - 04-11-2004
Hi,
My (extremely limited) understanding of game theory suggests that people often don't behave in what would seem to be the 'most logical' way when presented with a choice or decision, and especially not when more than one person is involved.
There are a few problems involved here. First (and it's been a long time, so anyone willing to refresh my memory is more than welcome) only zero sum two "person" games are proven to have a solution. If more than two parties are involved, or if the game is not zero sum (value can be created or destroyed) then there might be a solution and there might not.
Second, using a game theory strategy (where one exists) guarantees the best result (which might be negative) against a player also playing optimally. But when the very meaning of the concept of "best result" is defined differently by the two "players" (i.e, when one player is the "capitalistic West" and the other is the "Soviet Block"), it becomes difficult, if not impossible, to even define the games' goals. Which makes the calculation of a strategy rather tough.
Furthermore, even in a simple, zero sum, two-player game (say heads up poker) the "ideal" (as defined by game theory) strategy might not be the best. Against the same opponent, a player playing according to game theory would not do as well as a player who modified his strategy in accordance with the opponents weaknesses. Of course, that opens up a question which is hotly debated -- is the strategy of your opponent a "rule" of the game which should be included when doing the analysis? If so, then game theory always give the best strategy, but the game is always different. Useless perfection unless one has a great feel for the whole thing -- then it can lead to nice wins at the tables :)
--Pete
Bayesian Decision Theory - Vornzog - 04-11-2004
Hey Vandiablo,
Quote:I don't think this door switch game, tho, is the best example to illustrate Bayes Theorem, at least not for the way I learned Bayes.
IIRC the best examples are the ones using medical tests
See my first post - I also posted a similar 'disease test with false positive' sort of problem. I didn't work it out, just left it as an example for anyone who was interested to play with.
The reason I was looking at the door problem had to do with the fact that you need to know some extra information to make the best possible choice, and it is easiest to see that information in the door problem. That was the point of my 1000 doors instead of 3 example.
As for the way the game was actually played, I am happy to defer to anyone who originally watched it, as I wasn't so much alive in the 70's... Anything I know in this case, I know from Google, but I never assume that the pages it finds contain the last word on anything.
@Pete
Quote:But when the very meaning of the concept of "best result" is defined differently by the two "players" (i.e, when one player is the "capitalistic West" and the other is the "Soviet Block"), it becomes difficult, if not impossible, to even define the games' goals. Which makes the calculation of a strategy rather tough.
Hence my confusion as to how this could ever be applied rather than only pondered in an academic setting.
Quote:When supposed serious "intellectuals" do so, then I am reminded of one of my colleague's favorite expression: "metal masturbation".
I'm not really sure I'd go quite that far, but if it can't ever be applied, it does start to look like that. Academic speculations have their place, but inflicting them on your average college student (at least at my university) causes much unnecessary pain. If you can't apply it, and you are only going to hurt the students, it can't be good.
-V-
Bayesian Decision Theory - Vandiablo - 04-11-2004
Hey -V-
Doh! Mea culpa! Yep. I missed it because
A) I wasn't interested in the door or the veil or political science, so I ignored large portions of this thread -- I had thought you went from door to veil and I missed that one word line that said 'Disease' (and the text after), because
B.) I am guilty of not reading the whole thread (thought I could get away with it this time because of A above)
-V
I wonder if there's a -V+
Bayesian Decision Theory - Chaerophon - 04-29-2004
Just wanted to thank everyone for their insights on this thread. The collective input was extremely helpful, and my paper turned out quite well. Of course, what else should I expect from the Lounge?