In a generic finite normal form game with 2α + 1 Nash equilibria, at least α of the equilibria are nondegenerate mixed strategy equilibria (that is, they involve randomization by some players).
Faruk Gül, David Pearce, Ennio Stacchetti, (1993) A Bound on the Proportion of Pure Strategy Equilibria in Generic Games. Mathematics of Operations Research 18(3):548-552.
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