Equilibrium Points in N-Person Games

Summary

Proves that every finite game with any number of players has at least one equilibrium point, provided players may use mixed strategies.

Why it matters

It freed game theory from the two-player zero-sum setting that von Neumann’s minimax theorem covered. Because an equilibrium is guaranteed to exist in any finite game, equilibrium analysis became applicable to strategic situations generally, and the concept now carries Nash’s name across economics, biology, and multi-agent AI.