
Non-Cooperative Games (1950) [pdf] - thewisenerd
http://rbsc.princeton.edu/sites/default/files/Non-Cooperative_Games_Nash.pdf
======
notthemessiah
Seem neither Von Neumann nor Morgenstern were impressed by Nash's use of
Kakutani fixed-points to come up with equilibrium solutions, they see it as
impractical and difficult to apply, which it is because it assumes common
knowledge of the each player's expected utility. Since then Nash's theory has
been shown to be not very robust with uncertainty. Von Neumann was only
interested in practical applications of math and had no patience for axiomatic
formalist mathematics like that of Nash or Arrow-Debreu after being influenced
by Godel's impossibility theorem (Before that point, Von Neumann tried to
axiomize set theory and quantum mechanics).

[http://www.newyorker.com/news/john-cassidy/the-triumph-
and-f...](http://www.newyorker.com/news/john-cassidy/the-triumph-and-failure-
of-john-nashs-game-theory)

~~~
fileep
> Seem neither Von Neumann nor Morgenstern were impressed by Nash's use of
> Kakutani fixed-points to come up with equilibrium solutions, they see it as
> impractical and difficult to apply, which it is because it assumes common
> knowledge of the each player's expected utility.

Von Neumann would have thought no such thing! Nash used a fixed-point theorem
for an existence proof, which von Neumann himself had done in earlier work.

"Assumes common knowledge of each player's expected utility" doesn't make
sense in this context.

> Since then Nash's theory has been shown to be not very robust with
> uncertainty.

It's not clear which kind of uncertainty you're referring to here, but it
doesn't matter. Nash's theorem is a mathematical theorem, and the proof is
sound. It can't become less true over time.

~~~
oli5679
> Nash's theorem is a mathematical theorem, and the proof is sound. It can't
> become less true over time.

Nash proved the existence of the solution concept he defined. It is true that
at least one Nash Equilibrium exists for all games (with every information
structure). It is more subjective as to whether 'Nash Equilibria' are
particularly useful or interesting to specific classes of games.

Indeed, VN-M had already proposed a different solution concept that they
proved existed in a narrower range of games (best response equilibria in 2
player 0 sum games).

In games with asymmetric information structures, stricter equilibrium concepts
than Nash Equilibrium are often used, because there are typically a large
number of Nash Equilibria for any game.

For example, Bayesian Nash Equilibrium and Perfect Bayesian Equilibrium
restrict agents to forming beliefs in a 'Bayesian' manner, whilst the latter
also restricts their actions to also be BNE in subgames off the equilibrium
path of sequential games.

------
tux1968
More readable version:

[http://lcm.csa.iisc.ernet.in/gametheory/Classics/NCG.pdf](http://lcm.csa.iisc.ernet.in/gametheory/Classics/NCG.pdf)

~~~
mrcactu5
it is also a bit shorter - what really gets me are the hand-written equations
and constants.

------
jflowers45
This reminds me of the scene in A Beautiful Mind when they are talking about
Game Theory in the context of a group of men approaching a group of women at a
bar.

~~~
Chinjut
It should remind you of A Beautiful Mind. It's John Nash's doctoral thesis.

------
paulpauper
That's part of what makes the Nobel Prize interesting and unique. you
technically only need a single paper to win it

------
divbit
Really quite hard to read based on, I guess, the poor scan quality.. I wonder
if there is a better digitized version somewhere

~~~
tux1968
This looks better:

[http://lcm.csa.iisc.ernet.in/gametheory/Classics/NCG.pdf](http://lcm.csa.iisc.ernet.in/gametheory/Classics/NCG.pdf)

~~~
divbit
Much better thanks.

------
OtterCoder
This is very unintuitive to me. Most games have some sort of asymmetry built
in. For example one player usually goes first. In the game of nim, a clever
player can provably always dominate against any strategy if they move first.
That doesn't sound like an equilibrium to me...

~~~
oli5679
Your problem may be that the definition of Nash Equilibrium might not overlap
with your intuition of what 'equilibrium' should be.

A NE is just a strategy profile for every player of the game such that no
player would want to change her strategy profile if she knew the strategy
profile of all other players.

If the second player loses to the first player's strategy profile whatever she
does, that is still an equilibrium because she wouldn't gain from changing her
action to something else that also guarantees loss.

------
robinhoodexe
This really makes me appreciate TeX and friends. Writing equations, while just
one of the strengths of TeX, just looks so much better.

