Game Theory - Nash Equilibrium

Ohm

When the 21-year old John Nash wrote his 27-page dissertation outlining his "Nash Equilibrium" for strategic non-cooperative games, the impact was enormous. On the formal side, his existence proof was one of the first applications of Kakutani's fixed-point theorem later employed with so much gusto by Neo-Walrasians everywhere; on the conceptual side, he spawned much of the literature on non-cooperative game theory which has since grown at a prodigious rate - threatening, some claim, to overwhelm much of economics itself.
He prooved his theory through Mathematics. Is anyone familiar with the mathematics he has used?

phoenixthoth

i don't though i have heard the theory that all the big discoveries are made before age 30 which is contradicted by andrew wiles' proof of fermat's last theorem. i do know that if you try a web search, you get a huge list of results. there are books out there with his paper in it though i don't know the author. try amazoning nash's equilibrium theory.

does anyone know if a beautiful mind was correct? they said that it's basically like saying, "do what's best for yourself and the group." is that the right way to express nash's equilibrium theory? that sounds like a sound ethical precept to me.

some mathematicians consider his embedding theorem more important. does anyone know what the minimum m is so that if K is an n dimensional smooth manifold, then it can be embedded in R^m? is m=2n+1?

well, if the human self-awareness structure is 5D, then it can be embedded in 11D manifold. hmm... there are several people who believe that our human dimension is really 5D, in a manner of speaking, though those people are mainly spiritually oriented and not mathematically oriented and there's no proof.

does anyone know about coembeddability? if K is n-D and L is m-D, what is the minium o such that K and L are both embeddable in R^o?

c(m,n) be a function that gives this minimum.

if human awareness is 5D and the string theory manifold is 11D, then the dimensions of the universe might be c(5,11). any thoughts on what c(5,11) is regardless of the awareness reference? does it depend on the specifics of K and L?

if any of this is true, then euclid was really, in truth, on the right track after all.

"... Supposing that the bodies act upon the surrounding space causing curving of the same, it appears to my simple mind that the curved spaces must react on the bodies, and producing the opposite effects, straightening out the curves. Since action and reaction are coexistent, it follows that the supposed curvature of space is entirely impossible - But even if it existed it would not explain the motions of the bodies as observed. Only the existence of a field of forces can account for them and its assumptions dispenses with space curvature. ... " - Nikola Tesla

perhaps the noncurvature aspect of space-time is expressed in the nash embedding theorem which would say that there is a submanifold of some R^c(5,11), or some such, homeomorphic, or diffeomorphic, to space-time. interesting.

Thallium

Have you seen "A Beautiful Mind", Ohm? Russel Crow plays John Nash. A very good film, mostly about Nash's life of course.

I am also curious about the game theory. I have NO CLUE of what it is about! I never understood those letters c, d, f and so on and the numbers... What do they illustrate?

selfAdjoint

Here's an introductory sketch of Nash Equilibrium that I found by googling on Nash and equilibrium. There were 11,400 hits! Obviously a hot topic.