In Part 1 a duopoly example is given, and in Part 2 a brief proof of the existence of equilibrium points yields a simple proof of the main theorem of 2-person zero-sum games.
Research conducted by
Nash, John F., n-Person Games: An Example and a Proof. Santa Monica, CA: RAND Corporation, 1951. https://www.rand.org/pubs/research_memoranda/RM615.html.
Nash, John F., n-Person Games: An Example and a Proof, Santa Monica, Calif.: RAND Corporation, RM-615, 1951. As of September 08, 2021: https://www.rand.org/pubs/research_memoranda/RM615.html