From: Charles Hixson (charleshixsn@earthlink.net)
Date: Wed Feb 26 2003 - 08:14:27 MST
Anders Sandberg wrote:
>Sure, game theory is often an extreme oversimplification and especially
>in foras like this we tend to overuse it (I'm certainly guilty of that
>quite often). But at the other hand it also represents a well-understood
>formal structure which can derive implications of certain kinds of
>assumptions effectively; it is a modeling tool. The important thing to
>remember whenever one is making a model is whether the assumptions are
>complete enough to both lead to the right behavior and not leave out
>additional small complications that can change the resulting behavior
>qualitatively. The model should be as simple as possible, but not
>simpler.
>...
>
This is slightly wrong. A more accurate statement would be "The models
used in game theory are often extreme oversimplifications...". True,
they MUST be, because otherwise the math becomes computationally
intractable, but it's the model, and not the theory that are
oversimplifications. The theory quickly becomes complex beyond belief.
OTOH, if you mean zero-sum two person game theory, then yes, it is
often, even usually, an oversimplification. And that's the one that
gets used most often, because it's the easiest to figure out. (Not
because it's the most appropriate.)
Yet again, in a way this is like saying that physics is an
oversimplified model of the world... well, theoretically if you were to
model each particle (with appropriate degrees of uncertainty), and then
calculate forward the reactions... you would get the answer that
actually occurs. But it's a computationaly intractable approach, so
nobody does it (well... you also don't really have the initial
conditions). Note that you wouldn't get one answer, you would get a
sheave of answers. This is the same result that a full application of
game theory to a real situation would give. Granted, in the game theory
approach you might know the full relevant initial conditions, the answer
would still be a statistical distribution (except in certain very simple
cases).
This archive was generated by hypermail 2.1.5 : Wed Feb 26 2003 - 08:17:02 MST