Nash proves that if we allow mixed strategies, then every game with a finite number of players in which each player can choose from finitely many pure strategies has at least one Nash equilibrium.
Nash tõestab, et kui lubada segastrateegiaid, siis igal lõpliku mängijate arvuga mängul, kus valida on lõpliku arvu puhaste strateegiate vahel, on olemas vähemalt üks Nashi tasakaal.