TITLE: Why was John Nash's 1950 Game Theory paper such a big deal?
QUESTION [46 upvotes]: I'm trying to understand why John Nash's 1950 2-page paper that was published in PNAS was such a big deal. Unless I'm mistaken, the 1928 paper by John von Neumann demonstrated that all n-player non-cooperative and zero-sum games possess an equilibrium solution in terms of pure or mixed strategies. 
From what I understand, Nash used fixed point iteration to prove that non-zero-sum games would also have the analogous result. Why was this such a big deal in light of the earlier work by von Neumann? 
There are two references I provide that are good: One is this discussion on simple proofs of Nash's theorem and this one is a very well done (readable and accurate) survey of the history in PNAS.

REPLY [3 votes]: Let me start with my own view: 

The Nash equilibrium concept and the accompanying existence theorem is
  among the very few cornerstones in mathematical modeling of our
  reality .

Let me add a few more links. A paper by Ariel Rubinstein entitled "John Nash the master of economic modeling" and a document based on a seminar entitled: "The work of John Nash in Game theory." This includes the following quote from an earlier paper by Aumann. 
 
Nash equilibrium is probably the main reason for the "game-theoretic revolution" in theoretical economics.