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we've been using now for several weeks,
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except everywhere where before we saw a pure strategy,
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which was an S, I have replaced it with a P.
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So the same definition except
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I'm using mixed strategies instead of pure strategies.
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But an implication of our lesson is what?
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It's that if Pi* is part of a Nash Equilibrium,
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so if Pi* is a best response to what everyone else is doing, P-i*,
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then each of the pure strategies involved in Pi*
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must itself be a best response.
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So an implication of the lesson is, the lesson implies the following.
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If Pi* of a particular strategy is positive,