Project SherlockEst. Knowledge

Paper

1951

Non-Cooperative Games

John F. Nash

Proves, via Kakutani's fixed-point theorem, that every finite non-cooperative game has at least one equilibrium point in mixed strategies, and develops equilibrium as the general solution concept the 1950 note only sketched.

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FreeAdvancedlink checked 17 Sept 2026

Read these first

Not a difficulty warning — a route. These are in the library too.

Theory of Games and Economic BehaviorJohn von Neumann & Oskar Morgenstern, 1944Founds game theory as a mathematical discipline, formalising expected-utility under risk and solving two-person zero-sum games with the minimax theorem before extending the framework to coalitional n-person games.

If this is the wrong level

Too hard? Start hereEquilibrium Points in N-Person GamesJohn F. Nash, 1950Every finite game has at least one equilibrium point at which no player can gain by changing strategy alone, proved in barely two pages using a fixed-point theorem.

Filed under Game Theory & Mechanism Design in Economics.