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So the main lesson I want you to get from this
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is that not only did it matter that
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you need to put yourself in other people's shoes
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and think about what their payoffs are.
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You also need to put yourself into other people's shoes
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and think about how sophisticated are they at playing games.
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And you need to think about
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how sophisticated do they think you are at playing games.
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And you need to think about how sophisticated do they think
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that you think that they are at playing games and so on.
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This level of knowledge, these layers of knowledge,
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lead to very different play in the game.