Let me mention Nash's two famous contributions to game theory:

The notion of equilibrium of non cooperative games and a proof that every game has an equilibrium.

Nash's bargaining model his proposed axioms that a solution should satisfy, and his solution.

**More** Let me  copy my answer regarding Nash's work from a different question on the importance of Nash's work in game theory and economics. 

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"][1] and a document based on a seminar entitled: "[The work of John Nash in Game theory][2]." This includes the following quote from an earlier paper by Aumann. 


![enter image description here][3]  


  [1]: http://arielrubinstein.tau.ac.il/papers/47.pdf
  [2]: http://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/1994/nash-lecture.pdf
  [3]: https://i.sstatic.net/sAKY3.png

Nash equilibrium is probably the main reason for the "game-theoretic revolution" in theoretical economics.