{"id":"nash-equilibrium","domain":"applied","type":"Concept","title":"Nash Equilibrium","slug":"nash-equilibrium","url":"/mathematics/applied/nash-equilibrium/","proved":"1950, John Nash","summary":"A stable outcome where no player benefits from unilaterally changing strategy. Nash proved existence in every finite game (1950), aged 22. 1994 Nobel Memorial Prize.","added_to_codex":"2026-05-27","last_verified":"2026-05-27","sources":[{"tier":1,"citation":"Nash, J.F. (1950). Equilibrium points in n-person games. PNAS, 36(1), 48-49."},{"tier":1,"citation":"Nash, J.F. (1951). Non-cooperative games. Annals of Mathematics, 54(2), 286-295."},{"tier":2,"citation":"Osborne, M.J. and Rubinstein, A. (1994). A Course in Game Theory. MIT Press."},{"tier":3,"citation":"Nasar, S. (1998). A Beautiful Mind. Simon & Schuster."}],"relationships":[{"type":"central_concept_in","target":"game-theory","label":"Game Theory"},{"type":"uses","target":"topological-space","label":"Topological Space — Kakutani fixed-point theorem"},{"type":"uses","target":"probability","label":"Probability — mixed strategies"}],"entry_status":"live","reading_levels_available":["curious","exploring","deep_dive"],"completeness":1.0,"codex_version":"1.9"}