Hi there...

[Nash lover]

I'm going to have a lecture about game theory... I wan to talk about
noncooperative games with rational players and nash equilibrium. first
of all I need a clear definition of NASH EQUILIBRIUM... and then I need
a conclusion for the end of my lecture what should I do? what should I
write? please help me!!

[OHex]

As much as anything, Nash got the Nobel prize for showing that certain
finite games (a great many, actually) have an equilibrium point. This
is a state of affairs where even knowing the strategy on both sides,
neither side can gain by modifying their own strategy. In other words,
both sides have taken the optimum path. If you want to make it more
formal, you'll have to do it in the context of the other formalisms
you're using, so work it out.

The prize was for economics, where the importance was that there is a
way for vendors and purchasers (for instance) to strike a balance where
everyone wins, or at least that nobody gets cheated, and this can be
done in an open and transparent way. The existence of such equilibria
has had an important influence on international trade policies, for
instance.

Conclusions: maybe that last bit, but even better if you make up your
own.

++ kevin