This, however, is only a tendency. Some of the time, players select the
wrong moves. It would have been much wiser to assume that there are no
pure strategies, that all of them are mixed. Game Theory would have
done well to borrow mathematical techniques from quantum mechanics. For
instance: strategies could have been described as wave functions with
probability distributions. The same treatment could be accorded to the
cardinal utility function. Obviously, the highest ranking (smallest
ordinal) preference should have had the biggest probability attached to
it - or could be treated as the collapse event. But these are more or
less known, even trivial, objections. Some of them cannot be overcome.
We must idealize the world in order to be able to relate to it
scientifically at all. The idealization process entails the
incorporation of gross inaccuracies into the model and the ignorance of
other elements. The surprise is that the approximation yields results,
which tally closely with reality - in view of its mutilation, affected
by the model.
There are more serious problems, philosophical in nature.
It is generally agreed that "changing" the game can - and very often
does - move the players from a non-cooperative mode (leading to
Paretto-dominated results, which are never desirable) - to a
cooperative one.
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