# The Support of Mixed Strategies

This lecture defines the “support” of a mixed strategy.

Takeaway Points

1. A pure strategy is in the support of a mixed strategy if that pure strategy is played with positive probability according to the mixed strategy.
2. If a mixed strategy is played in a Nash equilibrium, all pure strategies in the support of that mixed strategy must yield an equal expected payoff. Otherwise, the player could profitably deviate to playing the specific strategy in the support that generated a higher payoff.

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